%   ORIGINAL: 'h4/thm/pair/pair_CASES_'
% 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: !x. ?q r. x = 'h4/const/pair/,' q r
%   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: !x. ?q r. x = 'h4/const/pair/,' q r
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_3f60811,V_3f60807]: ![F, G]: (![X]: s(V_3f60807,happ(s(fun(V_3f60811,V_3f60807),F),s(V_3f60811,X))) = s(V_3f60807,happ(s(fun(V_3f60811,V_3f60807),G),s(V_3f60811,X))) => s(fun(V_3f60811,V_3f60807),F) = s(fun(V_3f60811,V_3f60807),G))).
fof('h4/thm/pair/pair_CASES_', conjecture, ![A,B]: ![X]: ?[Q, R]: s('h4/type/pair/prod'(A,B),X) = s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,Q),s(B,R)))).
