Thm* s:(A+B) List, x:A. (x mapoutl(s))  (inl(x) s) | [mapoutl_member] |
Thm* s:(A+B) List, x:A. (x mapoutl(s))  ( y:A+B. (y s) & isl(y) & x = outl(y)) | [member_mapoutl] |
Thm* A,B:T List. no_repeats(T;A)  ( x:T. (x A)  (x B))  ( x:T. (x A) & (x B))  ||A|| < ||B|| | [length_less] |
Thm* A,B:T List. no_repeats(T;A)  ( x:T. (x A)  (x B))  ||A|| ||B|| | [length_le] |
Thm* a,b:T List, t:T. l_disjoint(T;b;[t / a])  (t b) & l_disjoint(T;b;a) | [l_disjoint_cons2] |
Thm* a,b:T List, t:T. l_disjoint(T;[t / a];b)  (t b) & l_disjoint(T;a;b) | [l_disjoint_cons] |
Thm* x:T, L:T List. (x rev(L))  (x L) | [member_reverse] |
Thm* L:T List, x,y:T. x before y L  ( A,B:T List. L = (A @ B) & (x A) & (y B)) | [l_before_decomp] |
Thm* A,B:T List, x,y:T. x before y A @ B  x before y A x before y B (x A) & (y B) | [l_before_append_iff] |
Thm* ( x,y:T. Dec(x = y))  ( s:T List, z:T. (z s)  ( s1,s2:T List. s = (s1 @ [z / s2]) & (z s1))) | [l_member_decomp2] |
Thm* s:T List, z:T. (z s)  ( s1,s2:T List. s = (s1 @ [z / s2])) | [l_member_decomp] |
Thm* i,j,k: . (k upto(i;j))  i k & k < j | [member_upto] |