({ Clicking on a green or brown colored
Method displays or hides the
Application of that
Method, and also displays or hides another Method or the
Reason in that
Paragraph. })
(^ ThingsAndFeatures ^)
[- Amalgamation -]
({ The thing whose features are all the features of features of +a will
be represented by +am/ +a. })
| +Df |
+Am |
[a [b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a |
| +1 |
+Ex |
) - [a [b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a
[b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a |
| +2 |
+Ab/ +1 |
) - +Am [b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a |
| +3 |
+Ex |
) - [b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a
= +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a |
| +Am1 | +Pr | +Tb// +2 +3 |
) - +Am = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a |
| +1 |
+Ex |
) - [c - ( +ft// +b +c +ft// +c +a - ( +ft// +b +e +ft// +e +a |
| +2 |
+Sm/ +1 |
) ]c ( +ft// +b +c +ft// +c +a - ( +ft// +b +e +ft// +e +a |
| +3 |
+Gn/ +2 |
[e ) ]c ( +ft// +b +c +ft// +c +a - ( +ft// +b +e +ft// +e +a |
| +4 |
+Fc/ +3 |
) ]c ( +ft// +b +c +ft// +c +a [e - ( +ft// +b +e +ft// +e +a |
| +5 |
+Tb/ +4 |
) ]c ( +ft// +b +c +ft// +c +a - - [e - ( +ft// +b +e +ft// +e +a |
| +6 |
+Sm/ +5 |
) ]c ( +ft// +b +c +ft// +c +a - ]e ( +ft// +b +e +ft// +e +a |
| +7 |
+Ex |
) - [e - ( +ft// +b +e +ft// +e +a - ( +ft// +b +c +ft// +c +a |
| +8 |
+Sm/ +7 |
) ]e ( +ft// +b +e +ft// +e +a - ( +ft// +b +c +ft// +c +a |
| +9 |
+Gn/ +8 |
[c ) ]e ( +ft// +b +e +ft// +e +a - ( +ft// +b +c +ft// +c +a |
| +10 |
+Fc/ +9 |
) ]e ( +ft// +b +e +ft// +e +a [c - ( +ft// +b +c +ft// +c +a |
| +11 |
+Tb/ +10 |
) ]e ( +ft// +b +e +ft// +e +a - - [c - ( +ft// +b +c +ft// +c +a |
| +12 |
+Sm/ +11 |
) ]e ( +ft// +b +e +ft// +e +a - ]c ( +ft// +b +c +ft// +c +a |
| +Am2 | +Pr | +Tb/// +Am1 +6 +12 |
) - +Am = +ft// +b +am/ +a ]e ( +ft// +b +e +ft// +e +a |
| +1 |
+Ex |
) - [c - ( +ft// +b +c +ft// +c +a - ( +ft// +b +d +ft// +d +a |
| +2 |
+Gn/ +1 |
[d ) - [c - ( +ft// +b +c +ft// +c +a - ( +ft// +b +d +ft// +d +a |
| +3 |
+Fc/ +2 |
) - [c - ( +ft// +b +c +ft// +c +a [d - ( +ft// +b +d +ft// +d +a |
| +4 |
+Tb/ +3 |
) - [c - ( +ft// +b +c +ft// +c +a - - [d - ( +ft// +b +d +ft// +d +a |
| +5 |
+Sm/ +4 |
) ]c ( +ft// +b +c +ft// +c +a - - [d - ( +ft// +b +d +ft// +d +a |
| +6 |
+Sm/ +5 |
) ]c ( +ft// +b +c +ft// +c +a - ]d ( +ft// +b +d +ft// +d +a |
| +7 |
+Ex |
) - [d - ( +ft// +b +d +ft// +d +a - ( +ft// +b +c +ft// +c +a |
| +8 |
+Gn/ +7 |
[c ) - [d - ( +ft// +b +d +ft// +d +a - ( +ft// +b +c +ft// +c +a |
| +9 |
+Fc/ +8 |
) - [d - ( +ft// +b +d +ft// +d +a [c - ( +ft// +b +c +ft// +c +a |
| +10 |
+Tb/ +9 |
) - [d - ( +ft// +b +d +ft// +d +a - - [c - ( +ft// +b +c +ft// +c +a |
| +11 |
+Sm/ +10 |
) ]d ( +ft// +b +d +ft// +d +a - - [c - ( +ft// +b +c +ft// +c +a |
| +12 |
+Sm/ +11 |
) ]d ( +ft// +b +d +ft// +d +a - ]c ( +ft// +b +c +ft// +c +a |
| +13 |
+Tb// +6 +12 |
= ]d ( +ft// +b +d +ft// +d +a ]c ( +ft// +b +c +ft// +c +a |
| +Am3 | +Pr | +Tb// +Am1 +13 |
) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a |
({ The relation of being the same is transmitted for amalgamations. })
| +1 |
+Ex |
) - [d - ( +ft// +c +d +ft// +d +b - ( +ft// +c +d +ft// +d +b |
| +1 |
+Ex |
) - [c ) - +sm// +a +b = +ft// +c +a +ft// +c +b ) - +sm// +a +b = +ft// +d +a +ft// +d +b |
| +2 |
+Gn/ +Sm2 |
[c ) - +sm// +a +b = +ft// +c +a +ft// +c +b |
| +2 | +Rp/ +Sm2 | +Tb// +1 +2 |
) - +sm// +a +b = +ft// +d +a +ft// +d +b |
| +3 |
+Tb// +1 +2 |
) - ( +sm// +a +b [d - ( +ft// +c +d +ft// +d +b - ( +ft// +c +d +ft// +d +a |
| +4 |
+Gn/ +3 |
[d ) - ( +sm// +a +b [d - ( +ft// +c +d +ft// +d +b - ( +ft// +c +d +ft// +d +a |
| +5 |
+Fc/ +4 |
) - ( +sm// +a +b [d - ( +ft// +c +d +ft// +d +b [d - ( +ft// +c +d +ft// +d +a |
| +6 |
+Tb/ +5 |
) - +sm// +a +b ) - - [d - ( +ft// +c +d +ft// +d +a - [d - ( +ft// +c +d +ft// +d +b |
| +7 |
+Sm/ +6 |
) - +sm// +a +b ) - ]d ( +ft// +c +d +ft// +d +a - [d - ( +ft// +c +d +ft// +d +b |
| +8 |
+Sm/ +7 |
) - +sm// +a +b ) - ]d ( +ft// +c +d +ft// +d +a ]d ( +ft// +c +d +ft// +d +b |
| +1 |
+Ex |
) - [a ) - +sm// +a +b ) - ]d ( +ft// +c +d +ft// +d +a ]d ( +ft// +c +d +ft// +d +b ) - +sm// +f +b ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +b |
| +2 |
+Gn/ +8 |
[a ) - +sm// +a +b ) - ]d ( +ft// +c +d +ft// +d +a ]d ( +ft// +c +d +ft// +d +b |
| +9 | +Rp/ +8 |
+Tb// +1 +2 |
) - +sm// +f +b ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +b |
| +1 |
+Ex |
) - [b ) - +sm// +f +b ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +b ) - +sm// +f +a ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +a |
| +2 |
+Gn/ +9 |
[b ) - +sm// +f +b ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +b |
| +10 | +Rp/ +9 |
+Tb// +1 +2 |
) - +sm// +f +a ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +a |
| +1 |
+Ex |
) - [f ) - +sm// +f +a ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +a ) - +sm// +b +a ) - ]d ( +ft// +c +d +ft// +d +b ]d ( +ft// +c +d +ft// +d +a |
| +2 |
+Gn/ +10 |
[f ) - +sm// +f +a ) - ]d ( +ft// +c +d +ft// +d +f ]d ( +ft// +c +d +ft// +d +a |
| +11 | +Rp/ +10 |
+Tb// +1 +2 |
) - +sm// +b +a ) - ]d ( +ft// +c +d +ft// +d +b ]d ( +ft// +c +d +ft// +d +a |
| +12 |
+Tb// +Sm3 +11 |
) - +sm// +a +b ) - ]d ( +ft// +c +d +ft// +d +b ]d ( +ft// +c +d +ft// +d +a |
| +13 |
+Tb// +8 +12 |
) - +sm// +a +b = ]d ( +ft// +c +d +ft// +d +a ]d ( +ft// +c +d +ft// +d +b |
| +1 |
+Ex |
) - [b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +2 |
+Gn/ +Am3 |
[b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a |
| +14 | +Rp/ +Am3 | +Tb// +1 +2 |
) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +1 |
+Ex |
) - [a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a ) - +Am = +ft// +c +am/ +b ]d ( +ft// +c +d +ft// +d +b |
| +2 |
+Gn/ +14 |
[a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +15 | +Rp/ +14 | +Tb// +1 +2 |
) - +Am = +ft// +c +am/ +b ]d ( +ft// +c +d +ft// +d +b |
| +16 |
+Tb/// +14 +13 +15 |
) - ( +Am +sm// +a +b = +ft// +c +am/ +a +ft// +c +am/ +b |
| +17 |
+Gn/ +16 |
[c ) - ( +Am +sm// +a +b = +ft// +c +am/ +a +ft// +c +am/ +b |
| +18 |
+Fc/ +17 |
) - ( +Am +sm// +a +b [c = +ft// +c +am/ +a +ft// +c +am/ +b |
| +Am4 | +Pr | +Ab/ +18 |
) - ( +Am +sm// +a +b +sm// +am/ +a +am/ +b |
| +1 |
+Ex |
) - [d - ( +ft// +c +d +ft// +d +a - ( +ft// +c +b +ft// +b +a |
| +2 |
+Sm/ +1 |
) ]d ( +ft// +c +d +ft// +d +a - ( +ft// +c +b +ft// +b +a |
| +1 |
+Ex |
) - [b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +2 |
+Gn/ +Am3 |
[b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a |
| +3 | +Rp/ +Am3 | +Tb// +1 +2 |
) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +Am5 | +Pr | +Tb// +2 +3 |
) - +Am ) - ( +ft// +c +b +ft// +b +a +ft// +c +am/ +a |
[- Union -]
| +Df |
+un// +a +b |
+am/ +th// +a +b |
({ The features of +un// +a +b are the combined features of +a
and +b. })
| +1 |
+Ex |
) - [b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +2 |
+Gn/ +Am3 |
[b ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a |
| +1 | +Rp/ +Am3 | +Tb// +1 +2 |
) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +1a |
+Ex |
) - [a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a ) - +Am = +ft// +c +am/ +th// +a +b ]d ( +ft// +c +d +ft// +d +th// +a +b |
| +2 |
+Gn/ +1 |
[a ) - +Am = +ft// +c +am/ +a ]d ( +ft// +c +d +ft// +d +a |
| +2 | +Rp/ +1 |
+Tb// +1a +2 |
) - +Am = +ft// +c +am/ +th// +a +b ]d ( +ft// +c +d +ft// +d +th// +a +b |
| +3 |
+Tb |
) ) +ft// +c +a +ft// +c +b - ( +ft// +c +d ) = +ft// +c +d +ft// +c +a = +ft// +c +d +ft// +c +b |
| +4 |
+Ex |
) - [c = +ft// +c +d +ft// +c +a = +ft// +c +d +ft// +c +a |
| +5 |
+Ex |
) - [c = +ft// +c +d +ft// +c +b = +ft// +c +d +ft// +c +b |
| +6 |
+Tb/// +3 +4 +5 |
) ) +ft// +c +a +ft// +c +b - ( +ft// +c +d
) [c = +ft// +c +d +ft// +c +a [c = +ft// +c +d +ft// +c +b |
| +7 |
+Ab/ +6 |
) ) +ft// +c +a +ft// +c +b - ( +ft// +c +d ) +sm// +d +a [c = +ft// +c +d +ft// +c +b |
| +8 |
+Ab/ +7 |
) ) +ft// +c +a +ft// +c +b - ( +ft// +c +d ) +sm// +d +a +sm// +d +b |
| +1 |
+Ex |
) - [c ) - +Th ) - ( +ft/ +a +ft/ +b = +ft// +c +th// +a +b ) +sm// +c +a +sm// +c +b ) - +Th ) - ( +ft/ +a +ft/ +b = +ft// +d +th// +a +b ) +sm// +d +a +sm// +d +b |
| +2 |
+Gn/ +Th1 |
[c ) - +Th ) - ( +ft/ +a +ft/ +b = +ft// +c +th// +a +b ) +sm// +c +a +sm// +c +b |
| +9 | +Rp/ +Th1 | +Tb// +1 +2 |
) - +Th ) - ( +ft/ +a +ft/ +b = +ft// +d +th// +a +b ) +sm// +d +a +sm// +d +b |
| +10 |
+Tb// +8 +9 |
) ) - +Th ) - ( +ft/ +a +ft/ +b ) +ft// +c +a +ft// +c +b - ( +ft// +c +d +ft// +d +th// +a +b |
| +11 |
+Gn/ +10 |
[d ) ) - +Th ) - ( +ft/ +a +ft/ +b ) +ft// +c +a +ft// +c +b - ( +ft// +c +d
+ft// +d +th// +a +b |
| +12 |
+Fc/ +11 |
) ) - +Th ) - ( +ft/ +a +ft/ +b ) +ft// +c +a +ft// +c +b [d - ( +ft// +c +d
+ft// +d +th// +a +b |
| +13 |
+Tb/ +12 |
) - +Th ) - ( +ft/ +a +ft/ +b
) - - [d - ( +ft// +c +d +ft// +d +th// +a +b ) +ft// +c +a +ft// +c +b |
| +14 |
+Sm/ +13 |
) - +Th ) - ( +ft/ +a +ft/ +b
) - ]d ( +ft// +c +d +ft// +d +th// +a +b ) +ft// +c +a +ft// +c +b |
| +15 |
+Ex |
) - [d - ( +ft// +c +d +ft// +d +th// +a +b - ( +ft// +c +a
+ft// +a +th// +a +b |
| +16 |
+Tb// +Th2 +15 |
) - +Th ) - ( +ft/ +a +ft/ +b
) - [d - ( +ft// +c +d +ft// +d +th// +a +b - +ft// +c +a |
| +17 |
+Ex |
) - [d - ( +ft// +c +d +ft// +d +th// +a +b - ( +ft// +c +b
+ft// +b +th// +a +b |
| +18 |
+Tb// +Th4 +17 |
) - +Th ) - ( +ft/ +a +ft/ +b
) - [d - ( +ft// +c +d +ft// +d +th// +a +b - +ft// +c +b |
| +19 |
+Tb// +16 +18 |
) - +Th ) - ( +ft/ +a +ft/ +b
) - [d - ( +ft// +c +d +ft// +d +th// +a +b - ) +ft// +c +a +ft// +c +b |
| +20 |
+Sm/ +19 |
) - +Th ) - ( +ft/ +a +ft/ +b ) ]d ( +ft// +c +d +ft// +d +th// +a +b
- ) +ft// +c +a +ft// +c +b |
| +21 |
+Tb// +14 +20 |
) - +Th ) - ( +ft/ +a +ft/ +b = ]d ( +ft// +c +d +ft// +d +th// +a +b ) +ft// +c +a +ft// +c +b |
| +22 |
+Tb// +2 +21 |
) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +am/ +th// +a +b ) +ft// +c +a +ft// +c +b |
| +Un1 | +Pr | +Ab/ +22 |
) - +Th ) - +Am
) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b |
({ +un// +a +b is symmetrical. })
| +1 |
+Ex |
) - [a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +b = +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b |
| +2 |
+Gn/ +Un1 |
[a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b |
| +1 | +Rp/ +Un1 | +Tb// +1 +2 |
) - +Th ) - +Am
) - ( +ft/ +g +ft/ +b = +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b |
| +1a |
+Ex |
) - [b ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +b = +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +a = +ft// +c +un// +g +a ) +ft// +c +g +ft// +c +a |
| +2 |
+Gn/ +1 |
[b ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +b = +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b |
| +2 | +Rp/ +1 | +Tb// +1a +2 |
) - +Th ) - +Am
) - ( +ft/ +g +ft/ +a = +ft// +c +un// +g +a ) +ft// +c +g +ft// +c +a |
| +1 |
+Ex |
) - [g ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +a = +ft// +c +un// +g +a ) +ft// +c +g +ft// +c +a ) - +Th ) - +Am ) - ( +ft/ +b +ft/ +a = +ft// +c +un// +b +a ) +ft// +c +b +ft// +c +a |
| +2a |
+Gn/ +2 |
[g ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +a = +ft// +c +un// +g +a ) +ft// +c +g +ft// +c +a |
| +3 | +Rp/ +2 | +Tb// +1 +2a |
) - +Th ) - +Am
) - ( +ft/ +b +ft/ +a = +ft// +c +un// +b +a ) +ft// +c +b +ft// +c +a |
| +4 |
+Tb// +Un1 +3 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b +ft// +c +un// +b +a |
| +5 |
+Gn/ +4 |
[c ) - ( +Th ( +Am ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b +ft// +c +un// +b +a |
| +6 |
+Fc/ +5 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b [c = +ft// +c +un// +a +b +ft// +c +un// +b +a |
| +Un2 | +Pr | +Ab/ +6 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b +sm// +un// +a +b +un// +b +a |
| +1 |
+Ex |
) - [b ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +a = +ft// +c +un// +a +a ) +ft// +c +a +ft// +c +a |
| +2 |
+Gn/ +Un1 |
[b ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b |
| +1 | +Rp/ +Un1 | +Tb// +1 +2 |
) - +Th ) - +Am
) - ( +ft/ +a +ft/ +a = +ft// +c +un// +a +a ) +ft// +c +a +ft// +c +a |
| +2 |
+Tb/ +1 |
) - ( +Th ( +Am +ft/ +a = +ft// +c +un// +a +a +ft// +c +a |
| +3 |
+Gn/ +2 |
[c ) - ( +Th ( +Am +ft/ +a = +ft// +c +un// +a +a +ft// +c +a |
| +4 |
+Fc/ +3 |
) - ( +Th ( +Am +ft/ +a [c = +ft// +c +un// +a +a +ft// +c +a |
| +Un3 | +Pr | +Ab/ +4 |
) - ( +Th ( +Am +ft/ +a +sm// +un// +a +a +a |
({ The proof of the following Fact about amalgamations uses +Un3. })
| +1 |
+Tb |
= +sm// +am/ +th// +a +a +a +sm// +am/ +th// +a +a +a |
| +2 |
+Ab/ +1 |
= +sm// +un// +a +a +a +sm// +am/ +th// +a +a +a |
| +3 |
+Tb// +Un3 +2 |
) - ( +Th ( +Am +ft/ +a +sm// +am/ +th// +a +a +a |
| +Am6 | +Pr | +Ab/ +3 |
) - ( +Th ( +Am +ft/ +a +sm// +am/ +th/ +a +a |
({ The relation of being the same is transmitted for unions. })
| +1 |
+Ex |
) - [b ) - +sm// +a +b = +ft// +c +a +ft// +c +b ) - +sm// +a +g = +ft// +c +a +ft// +c +g |
| +2 |
+Gn/ +Sm2 |
[b ) - +sm// +a +b = +ft// +c +a +ft// +c +b |
| +1 | +Rp/ +Sm2 | +Tb// +1 +2 |
) - +sm// +a +g = +ft// +c +a +ft// +c +g |
| +1 |
+Ex |
) - [a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +g +ft/ +b = +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b |
| +2 |
+Gn/ +Un1 |
[a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b |
| +2 | +Rp/ +Un1 | +Tb// +1 +2 |
) - +Th ) - +Am ) - ( +ft/ +g +ft/ +b
= +ft// +c +un// +g +b ) +ft// +c +g +ft// +c +b |
| +2a |
+Tb// +Sm3 +Ft2 |
) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b |
| +1 |
+Ex |
) - [b ) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b ) - +Th ) - ( +ft/ +a +sm// +a +g +ft/ +g |
| +2 |
+Gn/ +2a |
[b ) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b |
| +2b | +Rp/ +2a | +Tb// +1 +2 |
) - +Th ) - ( +ft/ +a +sm// +a +g +ft/ +g |
| +3 |
+Tb//// +Un1 +1 +2 +2b |
) - ( +Th ( +Am ( +ft/ +a ( +ft/ +b +sm// +a +g
= +ft// +c +un// +a +b +ft// +c +un// +g +b |
| +4 |
+Gn/ +3 |
[c ) - ( +Th ( +Am ( +ft/ +a ( +ft/ +b +sm// +a +g
= +ft// +c +un// +a +b +ft// +c +un// +g +b |
| +5 |
+Fc/ +4 |
) - ( +Th ( +Am ( +ft/ +a ( +ft/ +b +sm// +a +g
[c = +ft// +c +un// +a +b +ft// +c +un// +g +b |
| +6 |
+Tb/ +5 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g
[c = +ft// +c +un// +a +b +ft// +c +un// +g +b |
| +Un4 | +Pr | +Ab/ +6 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g +sm// +un// +a +b +un// +g +b |
| +1 |
+Ex |
) - [a ) - ( +Th ( +Am ( +ft/ +a +ft/ +b +sm// +un// +a +b +un// +b +a ) - ( +Th ( +Am ( +ft/ +g +ft/ +b +sm// +un// +g +b +un// +b +g |
| +2 |
+Gn/ +Un2 |
[a ) - ( +Th ( +Am ( +ft/ +a +ft/ +b +sm// +un// +a +b +un// +b +a |
| +1 | +Rp/ +Un2 | +Tb// +1 +2 |
) - ( +Th ( +Am ( +ft/ +g +ft/ +b +sm// +un// +g +b +un// +b +g |
| +1 |
+Ex |
) - [b ) - ( +sm// +a +b +sm// +b +d +sm// +a +d ) - ( +sm// +a +h +sm// +h +d +sm// +a +d |
| +2 |
+Gn/ +Sm4 |
[b ) - ( +sm// +a +b +sm// +b +d +sm// +a +d |
| +2 | +Rp/ +Sm4 | +Tb// +1 +2 |
) - ( +sm// +a +h +sm// +h +d +sm// +a +d |
| +1 |
+Ex |
) - [a ) - ( +sm// +a +h +sm// +h +d +sm// +a +d ) - ( +sm// +un// +a +b +h +sm// +h +d +sm// +un// +a +b +d |
| +2a |
+Gn/ +2 |
[a ) - ( +sm// +a +h +sm// +h +d +sm// +a +d |
| +3 | +Rp/ +2 | +Tb// +1 +2a |
) - ( +sm// +un// +a +b +h +sm// +h +d
+sm// +un// +a +b +d |
| +1 |
+Ex |
) - [h ) - ( +sm// +un// +a +b +h +sm// +h +d +sm// +un// +a +b +d ) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +d +sm// +un// +a +b +d |
| +2 |
+Gn/ +3 |
[h ) - ( +sm// +un// +a +b +h +sm// +h +d +sm// +un// +a +b +d |
| +4 | +Rp/ +3 | +Tb// +1 +2 |
) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +d
+sm// +un// +a +b +d |
| +1 |
+Ex |
) - [d ) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +d +sm// +un// +a +b +d ) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +un// +b +g +sm// +un// +a +b +un// +b +g |
| +2 |
+Gn/ +4 |
[d ) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +d +sm// +un// +a +b +d |
| +5 | +Rp/ +4 |
+Tb// +1 +2 |
) - ( +sm// +un// +a +b +un// +g +b +sm// +un// +g +b +un// +b +g
+sm// +un// +a +b +un// +b +g |
| +5a |
+Tb// +Sm3 +Ft2 |
) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b |
| +1 |
+Ex |
) - [b ) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b ) - +Th ) - ( +ft/ +a +sm// +a +g +ft/ +g |
| +2 |
+Gn/ +5a |
[b ) - +Th ) - ( +ft/ +a +sm// +a +b +ft/ +b |
| +5b | +Rp/ +5a | +Tb// +1 +2 |
) - +Th ) - ( +ft/ +a +sm// +a +g +ft/ +g |
| +6 |
+Tb//// +Un4 +1 +5 +5b |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g +sm// +un// +a +b +un// +b +g |
| +6a |
+Tb/ +Sm3 |
) - +sm// +a +b +sm// +b +a |
| +1 |
+Ex |
) - [a ) - +sm// +a +b +sm// +b +a ) - +sm// +h +b +sm// +b +h |
| +2 |
+Gn/ +6a |
[a ) - +sm// +a +b +sm// +b +a |
| +7 | +Rp/ +6a | +Tb// +1 +2 |
) - +sm// +h +b +sm// +b +h |
| +1 |
+Ex |
) - [b ) - +sm// +h +b +sm// +b +h ) - +sm// +h +i +sm// +i +h |
| +2 |
+Gn/ +7 |
[b ) - +sm// +h +b +sm// +b +h |
| +8 | +Rp/ +7 | +Tb// +1 +2 |
) - +sm// +h +i +sm// +i +h |
| +1 |
+Ex |
) - [h ) - +sm// +h +i +sm// +i +h ) - +sm// +un// +a +b +i +sm// +i +un// +a +b |
| +2 |
+Gn/ +8 |
[h ) - +sm// +h +i +sm// +i +h |
| +9 | +Rp/ +8 | +Tb// +1 +2 |
) - +sm// +un// +a +b +i +sm// +i +un// +a +b |
| +1 |
+Ex |
) - [i ) - +sm// +un// +a +b +i +sm// +i +un// +a +b ) - +sm// +un// +a +b +un// +b +a +sm// +un// +b +a +un// +a +b |
| +2 |
+Gn/ +9 |
[i ) - +sm// +un// +a +b +i +sm// +i +un// +a +b |
| +10 | +Rp/ +9 |
+Tb// +1 +2 |
) - +sm// +un// +a +b +un// +b +a +sm// +un// +b +a +un// +a +b |
| +1 |
+Ex |
) - [a ) - ( +sm// +a +h +sm// +h +d +sm// +a +d ) - ( +sm// +un// +b +a +h +sm// +h +d +sm// +un// +b +a +d |
| +2a |
+Gn/ +2 |
[a ) - ( +sm// +a +h +sm// +h +d +sm// +a +d |
| +11 | +Rp/ +2 | +Tb// +1 +2a |
) - ( +sm// +un// +b +a +h +sm// +h +d
+sm// +un// +b +a +d |
| +1 |
+Ex |
) - [h ) - ( +sm// +un// +b +a +h +sm// +h +d +sm// +un// +b +a +d ) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +d +sm// +un// +b +a +d |
| +2 |
+Gn/ +11 |
[h ) - ( +sm// +un// +b +a +h +sm// +h +d +sm// +un// +b +a +d |
| +12 | +Rp/ +11 | +Tb// +1 +2 |
) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +d
+sm// +un// +b +a +d |
| +1 |
+Ex |
) - [d ) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +d +sm// +un// +b +a +d ) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +un// +b +g +sm// +un// +b +a +un// +b +g |
| +2 |
+Gn/ +12 |
[d ) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +d +sm// +un// +b +a +d |
| +13 | +Rp/ +12 |
+Tb// +1 +2 |
) - ( +sm// +un// +b +a +un// +a +b +sm// +un// +a +b +un// +b +g
+sm// +un// +b +a +un// +b +g |
| +Un5 | +Pr | +Tb//// +Un2 +6 +10 +13 |
) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g +sm// +un// +b +a +un// +b +g |
[- Division -]
({ For any thing +a, the thing whose features are all the things
that have exactly one feature, and are such that their one and only feature is a
feature of +a, will be called the division of +a, and
represented by +dv/ +a. })
| +Df |
+Dv |
[a [b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c |
| +1 |
+Ex |
) - [a [b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c
[b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c |
| +2 |
+Ab/ +1 |
) - +Dv
[b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c |
| +3 |
+Ex |
) - [b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c
= +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c |
| +Dv1 | +Pr | +Tb// +2 +3 |
) - +Dv = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c |
({ The Adverb can be changed as in the following example. })
| +1 |
+Ex |
) - [c - ( +ft// +c +a +sm// +b +th/ +c - ( +ft// +g +a +sm// +b +th/ +g |
| +2 |
+Gn/ +1 |
[g ) - [c - ( +ft// +c +a +sm// +b +th/ +c - ( +ft// +g +a +sm// +b +th/ +g |
| +3 |
+Fc/ +2 |
) - [c - ( +ft// +c +a +sm// +b +th/ +c [g - ( +ft// +g +a +sm// +b +th/ +g |
| +4 |
+Ex |
) - [g - ( +ft// +g +a +sm// +b +th/ +g - ( +ft// +c +a +sm// +b +th/ +c |
| +5 |
+Gn/ +4 |
[c ) - [g - ( +ft// +g +a +sm// +b +th/ +g - ( +ft// +c +a +sm// +b +th/ +c |
| +6 |
+Fc/ +5 |
) - [g - ( +ft// +g +a +sm// +b +th/ +g [c - ( +ft// +c +a +sm// +b +th/ +c |
| +7 |
+Tb// +3 +6 |
= - [g - ( +ft// +g +a +sm// +b +th/ +g - [c - ( +ft// +c +a +sm// +b +th/ +c |
| +8 |
+Sm/ +7 |
= ]g ( +ft// +g +a +sm// +b +th/ +g - [c - ( +ft// +c +a +sm// +b +th/ +c |
| +9 |
+Sm/ +8 |
= ]g ( +ft// +g +a +sm// +b +th/ +g ]c ( +ft// +c +a +sm// +b +th/ +c |
| +Dv2 | +Pr | +Tb// +Dv1 +9 |
) - +Dv = +ft// +b +dv/ +a ]g ( +ft// +g +a +sm// +b +th/ +g |
| +1 |
+Ex |
) - [g - ( +ft// +g +a +sm// +b +th/ +g - ( +ft// +g +a +sm// +b +th/ +g |
| +2 |
+Sm/ +1 |
) ]g ( +ft// +g +a +sm// +b +th/ +g - ( +ft// +g +a +sm// +b +th/ +g |
| +3 |
+Tb// +Dv2 +2 |
) - +Dv ) - ( +ft// +g +a +sm// +b +th/ +g +ft// +b +dv/ +a |
| +1 |
+Ex |
) - [b ) - +Dv ) - ( +ft// +g +a +sm// +b +th/ +g +ft// +b +dv/ +a ) - +Dv ) - ( +ft// +g +a +sm// +th/ +g +th/ +g +ft// +th/ +g +dv/ +a |
| +2 |
+Gn/ +3 |
[b ) - +Dv ) - ( +ft// +g +a +sm// +b +th/ +g +ft// +b +dv/ +a |
| +4 | +Rp/ +3 |
+Tb// +1 +2 |
) - +Dv ) - ( +ft// +g +a +sm// +th/ +g +th/ +g +ft// +th/ +g +dv/ +a |
| +1 |
+Ex |
) - [a +sm// +a +a +sm// +th/ +g +th/ +g |
| +2 |
+Gn/ +Sm1 |
[a +sm// +a +a |
| +5 | +Rp/ +Sm1 | +Tb// +1 +2 |
+sm// +th/ +g +th/ +g |
| +Dv3 | +Pr | +Tb// +4 +5 |
) - +Dv ) - +ft// +g +a +ft// +th/ +g +dv/ +a |
({ If +a is a feature, then +th/ +a is a feature. })
| +1 |
+Ex |
) - [a ) - +Dv ) - +ft// +g +a +ft// +th/ +g +dv/ +a ) - +Dv ) - +ft// +g +th/ +g +ft// +th/ +g +dv/ +th/ +g |
| +2 |
+Gn/ +Dv3 |
[a ) - +Dv ) - +ft// +g +a +ft// +th/ +g +dv/ +a |
| +1 | +Rp/ +Dv3 | +Tb// +1 +2 |
) - +Dv ) - +ft// +g +th/ +g +ft// +th/ +g +dv/ +th/ +g |
| +1a |
+Ex |
) - [g ) - +Dv ) - +ft// +g +th/ +g +ft// +th/ +g +dv/ +th/ +g ) - +Dv ) - +ft// +a +th/ +a +ft// +th/ +a +dv/ +th/ +a |
| +2 |
+Gn/ +1 |
[g ) - +Dv ) - +ft// +g +th/ +g +ft// +th/ +g +dv/ +th/ +g |
| +2 | +Rp/ +1 | +Tb// +1a +2 |
) - +Dv ) - +ft// +a +th/ +a +ft// +th/ +a +dv/ +th/ +a |
| +3 |
+Tb// +Th11 +2 |
) - ( +Th +Dv ) - +ft/ +a +ft// +th/ +a +dv/ +th/ +a |
| +1 |
+Ex |
) - [b - +ft// +th/ +a +b - +ft// +th/ +a +dv/ +th/ +a |
| +2 |
+Tb// +1 +3 |
) - ( +Th +Dv ) - +ft/ +a - [b - +ft// +th/ +a +b |
| +4 | +Sc/ +3 | +Sm/ +2 |
) - ( +Th +Dv ) - +ft/ +a ]b +ft// +th/ +a +b |
| +Th18 | +Pr | +Ab/ +4 |
) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a |
| +1 |
+Ex |
) - [a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +b = +ft// +c +un// +th/ +a +b ) +ft// +c +th/ +a +ft// +c +b |
| +2 |
+Gn/ +Un1 |
[a ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b |
| +1 | +Rp/ +Un1 |
+Tb// +1 +2 |
) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +b = +ft// +c +un// +th/ +a +b
) +ft// +c +th/ +a +ft// +c +b |
| +1a |
+Ex |
) - [b ) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +b = +ft// +c +un// +th/ +a +b ) +ft// +c +th/ +a +ft// +c +b ) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +th/ +b = +ft// +c +un// +th/ +a +th/ +b ) +ft// +c +th/ +a +ft// +c +th/ +b |
| +2 |
+Gn/ +1 |
[b ) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +b = +ft// +c +un// +th/ +a +b ) +ft// +c +th/ +a +ft// +c +b |
| +2 | +Rp/ +1 |
+Tb// +1a +2 |
) - +Th ) - +Am ) - ( +ft/ +th/ +a +ft/ +th/ +b = +ft// +c +un// +th/ +a +th/ +b
) +ft// +c +th/ +a +ft// +c +th/ +b |
| +1 |
+Ex |
) - [a ) - +Th ) - +ft/ +a = +ft// +c +th/ +a +sm// +c +a ) - +Th ) - +ft/ +b = +ft// +c +th/ +b +sm// +c +b |
| +2 |
+Gn/ +Th10 |
[a ) - +Th ) - +ft/ +a = +ft// +c +th/ +a +sm// +c +a |
| +3 | +Rp/ +Th10 | +Tb// +1 +2 |
) - +Th ) - +ft/ +b = +ft// +c +th/ +b +sm// +c +b |
| +4 |
+Tb// +Th18 +2 |
) - ( +Th ( +Am +Dv ) - ( +ft/ +a +ft/ +th/ +b
= +ft// +c +un// +th/ +a +th/ +b ) +ft// +c +th/ +a +ft// +c +th/ +b |
| +1 |
+Ex |
) - [a ) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a ) - ( +Th +Dv ) - +ft/ +b +ft/ +th/ +b |
| +2 |
+Gn/ +Th18 |
[a ) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a |
| +5 | +Rp/ +Th18 | +Tb// +1 +2 |
) - ( +Th +Dv ) - +ft/ +b +ft/ +th/ +b |
| +6 |
+Tb// +4 +5 |
) - ( +Th ( +Am +Dv ) - ( +ft/ +a +ft/ +b
= +ft// +c +un// +th/ +a +th/ +b ) +ft// +c +th/ +a +ft// +c +th/ +b |
| +7 |
+Tb//// +Th1 +Th10 +3 +6 |
) - ( +Th ( +Am ( +Dv ( +ft/ +a +ft/ +b = +ft// +c +un// +th/ +a +th/ +b +ft// +c +th// +a +b |
| +8 |
+Gn/ +7 |
[c ) - ( +Th ( +Am ( +Dv ( +ft/ +a +ft/ +b = +ft// +c +un// +th/ +a +th/ +b +ft// +c +th// +a +b |
| +9 |
+Fc/ +8 |
) - ( +Th ( +Am ( +Dv ( +ft/ +a +ft/ +b [c = +ft// +c +un// +th/ +a +th/ +b +ft// +c +th// +a +b |
| +Th19 | +Pr | +Ab/ +9 |
) - ( +Th ( +Am ( +Dv ( +ft/ +a +ft/ +b +sm// +un// +th/ +a +th/ +b +th// +a +b |
| +1 |
+Ex |
) - [a ) - ( +Th ( +ft/ +a ( +ft/ +b +ft/ +c ) - +sm// +th// +a +b +th/ +c +sm// +a +b ) - ( +Th ( +ft/ +0 ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +b +th/ +c +sm// +0 +b |
| +2 |
+Gn/ +Th14 |
[a ) - ( +Th ( +ft/ +a ( +ft/ +b +ft/ +c ) - +sm// +th// +a +b +th/ +c +sm// +a +b |
| +1 | +Rp/ +Th14 | +Tb// +1 +2 |
) - ( +Th ( +ft/ +0 ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +b +th/ +c +sm// +0 +b |
| +2 |
+Tb// +Nf4 +1 |
) - ( +Th ( +Nf ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +b +th/ +c +sm// +0 +b |
| +1 |
+Ex |
) - [b ) - ( +Th ( +Nf ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +b +th/ +c +sm// +0 +b ) - ( +Th ( +Nf ( +ft/ +th/ +b +ft/ +c ) - +sm// +th// +0 +th/ +b +th/ +c +sm// +0 +th/ +b |
| +2a |
+Gn/ +2 |
[b ) - ( +Th ( +Nf ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +b +th/ +c +sm// +0 +b |
| +3 | +Rp/ +2 | +Tb// +1 +2a |
) - ( +Th ( +Nf ( +ft/ +th/ +b +ft/ +c ) - +sm// +th// +0 +th/ +b +th/ +c +sm// +0 +th/ +b |
| +1 |
+Ex |
) - [a ) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a ) - ( +Th +Dv ) - +ft/ +b +ft/ +th/ +b |
| +2 |
+Gn/ +Th18 |
[a ) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a |
| +4 | +Rp/ +Th18 | +Tb// +1 +2 |
) - ( +Th +Dv ) - +ft/ +b +ft/ +th/ +b |
| +5 |
+Tb// +3 +4 |
) - ( +Nf ( +Th ( +Dv ( +ft/ +b +ft/ +c ) - +sm// +th// +0 +th/ +b +th/ +c +sm// +0 +th/ +b |
| +1 |
+Ex |
) - [a ) - ( +Nf +Th ) - +ft/ +a - +sm// +0 +th/ +a ) - ( +Nf +Th ) - +ft/ +b - +sm// +0 +th/ +b |
| +2 |
+Gn/ +Th16 |
[a ) - ( +Nf +Th ) - +ft/ +a - +sm// +0 +th/ +a |
| +6 | +Rp/ +Th16 | +Tb// +1 +2 |
) - ( +Nf +Th ) - +ft/ +b - +sm// +0 +th/ +b |
| +Th20 | +Pr | +Tb// +5 +6 |
) - ( +Nf ( +Th ( +Dv ( +ft/ +b +ft/ +c - +sm// +th// +0 +th/ +b +th/ +c |
(_ CrossUnion _)
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