%   ORIGINAL: 'h4/thm/nets/MTOP_TENDS_UNIQ_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !x1 x0 x g d. 'h4/const/nets/dorder' g ==> 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) /\ 'h4/const/nets/tends' x x1 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) ==> x0 = x1
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !x1 x0 x g d. 'h4/const/nets/dorder' g ==> 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) /\ 'h4/const/nets/tends' x x1 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) ==> x0 = x1
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f63836,V_3f63832]: ![F, G]: (![X]: s(V_3f63832,happ(s(fun(V_3f63836,V_3f63832),F),s(V_3f63836,X))) = s(V_3f63832,happ(s(fun(V_3f63836,V_3f63832),G),s(V_3f63836,X))) => s(fun(V_3f63836,V_3f63832),F) = s(fun(V_3f63836,V_3f63832),G))).
fof('h4/thm/nets/MTOP_TENDS_UNIQ_', conjecture, ![B,A]: ![X1, X0, X, G, D]: (p(s(bool,'h4/const/nets/dorder'(s(fun(B,fun(B,bool)),G)))) => ((p(s(bool,'h4/const/nets/tends'(s(fun(B,A),X),s(A,X0),s('h4/type/pair/prod'('h4/type/topology/topology'(A),fun(B,fun(B,bool))),'h4/const/pair/,'(s('h4/type/topology/topology'(A),'h4/const/topology/mtop'(s('h4/type/topology/metric'(A),D))),s(fun(B,fun(B,bool)),G)))))) & p(s(bool,'h4/const/nets/tends'(s(fun(B,A),X),s(A,X1),s('h4/type/pair/prod'('h4/type/topology/topology'(A),fun(B,fun(B,bool))),'h4/const/pair/,'(s('h4/type/topology/topology'(A),'h4/const/topology/mtop'(s('h4/type/topology/metric'(A),D))),s(fun(B,fun(B,bool)),G))))))) => s(A,X0) = s(A,X1)))).
