graph 1 1 Sections Graphs Doc

Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive)

is mentioned by

Thm* L:(A+B) List, a:A. mapoutl(L) = [a] (L1,L2:(A+B) List. L = (L1 @ [inl(a)] @ L2) & mapoutl(L1) = nil & mapoutl(L2) = nil)[mapoutl_is_singleton]
Thm* L:(A+B) List, l1,l2:A List. mapoutl(L) = (l1 @ l2) (L1,L2:(A+B) List. L = (L1 @ L2) & mapoutl(L1) = l1 & mapoutl(L2) = l2)[mapoutl_is_append]
Thm* L1,L2:(A+B) List. mapoutl(L1 @ L2) ~ (mapoutl(L1) @ mapoutl(L2))[mapoutl_append]
Thm* l1,l2:T List. no_repeats(T;l1 @ l2) l_disjoint(T;l1;l2) & no_repeats(T;l1) & no_repeats(T;l2)[no_repeats_append_iff]
Thm* a,b,c:T List. l_disjoint(T;c;a @ b) l_disjoint(T;c;a) & l_disjoint(T;c;b)[l_disjoint_append2]
Thm* a,b,c:T List. l_disjoint(T;a @ b;c) l_disjoint(T;a;c) & l_disjoint(T;b;c)[l_disjoint_append]
Thm* L:T List, x,y:T. x before y L (L1,L2,L3:T List. L = (L1 @ [x] @ L2 @ [y] @ L3))[l_before-iff]
Thm* x,z,y,w:T List. ||x|| = ||z|| ||y|| = ||w|| (x @ y) = (z @ w) x = z & y = w[append_one_one]
Thm* a,b:T List, x:T. [x] = (a @ b) a = nil & b = [x] b = nil & a = [x][append_is_singleton]
Thm* a,c,b,d:T List. (a @ b) = (c @ d) (e:T List. a = (c @ e) & d = (e @ b) c = (a @ e) & b = (e @ d))[equal_appends]
Thm* P:(T), L2,L1:T List. list_accum(l,x.if P(x) [x / l] else l fi;L1;L2) ~ (rev(filter(P;L2)) @ L1)[filter_list_accum]
Thm* a,b,c:Top List. ((a @ b) @ c) ~ (a @ b @ c)[append_assoc_sq]
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* C,A,B:T List. C A @ B (A',B':T List. C = (A' @ B') & A' A & B' B)[sublist_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* l1,l2:Top List, f,y:Top. list_accum(x,a.f(x,a);y;l1 @ l2) ~ list_accum(x,a.f(x,a);list_accum(x,a.f(x,a);y;l1);l2)[list_accum_append]
Thm* L:Top List, n:{0...||L||}. (firstn(n;L) @ nth_tl(n;L)) ~ L[append_firstn_lastn_sq]
Thm* x,y,z:T List. (x @ z) = (y @ z) x = y[equal_append_front]
Thm* l1,l2:T List. nil = (l1 @ l2) l1 = nil & l2 = nil[nil_is_append]
Thm* s:T List. 0 < ||s|| (s ~ (firstn(||s||-1;s) @ [s[(||s||-1)]]))[list-decomp-last]
Thm* i,j,k:. ij jk (upto(i;k) ~ (upto(i;j) @ upto(j;k)))[append_upto]
Thm* P:(T), T':Type, f:({x:T| P(x) }T'), L1,L2:T List. mapfilter(f;P;L1 @ L2) = (mapfilter(f;P;L1) @ mapfilter(f;P;L2))[mapfilter_append]
Thm* x1,z,x2,x3:T List. ||x1|| = ||z|| (x1 @ x2) = (z @ x3) x1 = z & x2 = x3[equal_appends_eq]
Thm* x1,z,x2,x3:T List. ||z||||x1|| (x1 @ x2) = (z @ x3) (z':T List. x1 = (z @ z') & x3 = (z' @ x2))[equal_appends_case2]
Thm* x1,z,x2,x3:T List. ||x1||||z|| (x1 @ x2) = (z @ x3) (z':T List. z = (x1 @ z') & x2 = (z' @ x3))[equal_appends_case1]

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