%   ORIGINAL: 'h4/thm/pair/PAIR_FST_SND_EQ_'
% 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: !p q. p = q <=> 'h4/const/pair/FST' p = 'h4/const/pair/FST' q /\ 'h4/const/pair/SND' p = 'h4/const/pair/SND' q
%   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: !p q. p = q <=> 'h4/const/pair/FST' p = 'h4/const/pair/FST' q /\ 'h4/const/pair/SND' p = 'h4/const/pair/SND' q
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_3f60886,V_3f60882]: ![F, G]: (![X]: s(V_3f60882,happ(s(fun(V_3f60886,V_3f60882),F),s(V_3f60886,X))) = s(V_3f60882,happ(s(fun(V_3f60886,V_3f60882),G),s(V_3f60886,X))) => s(fun(V_3f60886,V_3f60882),F) = s(fun(V_3f60886,V_3f60882),G))).
fof('h4/thm/pair/PAIR_FST_SND_EQ_', conjecture, ![A,B]: ![P, Q]: (s('h4/type/pair/prod'(A,B),P) = s('h4/type/pair/prod'(A,B),Q) <=> (s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),P))) = s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),Q))) & s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),P))) = s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),Q)))))).
