Rank | Theorem | Name |
4 | Thm* DivGraph_2 DivGraph_1 | [div-graph-iso] |
cites |
1 | Thm* G,H,K:Graph. G H  H K  G K | [graph-isomorphic_transitivity] |
3 | Thm* a,b: , n:  . n a = n b  a = b | [mul_cancel_in_eq] |
2 | Thm* f:(A B A). ( a:A, b1,b2:B. f(a,b1) = f(a,b2)  b1 = b2)  ( a,a':A. Dec( b:B. a' = f(a,b)))  Graph(a:A -- > f(a,b) | b:B) Graph(a,a':A. b:B. a' = f(a,b)) | [fun-graph-rel-graph] |
3 | Thm* a,b: . a b > 0  a > 0 & b > 0 a < 0 & b < 0 | [pos_mul_arg_bounds] |
1 | Thm* R1,R2:(T T Prop). ( x,y:T. R1(x,y)  R2(x,y))  Graph(x,y:T. R1(x,y)) Graph(x,y:T. R2(x,y)) | [rel-graph_functionality] |