%   ORIGINAL: 'h4/thm/pair/pair_case_cong_'
% 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: !'f\'' M 'M\'' f. M = 'M\'' /\ (!x y. 'M\'' = 'h4/const/pair/,' x y ==> f x y = 'f\'' x y) ==> 'h4/const/pair/pair_CASE' M f = 'h4/const/pair/pair_CASE' 'M\'' 'f\''
%   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: !'f\'' M 'M\'' f. M = 'M\'' /\ (!x y. 'M\'' = 'h4/const/pair/,' x y ==> happ (happ f x) y = happ (happ 'f\'' x) y) ==> 'h4/const/pair/pair_CASE' M f = 'h4/const/pair/pair_CASE' 'M\'' 'f\''
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_3f61686,V_3f61682]: ![F, G]: (![X]: s(V_3f61682,happ(s(fun(V_3f61686,V_3f61682),F),s(V_3f61686,X))) = s(V_3f61682,happ(s(fun(V_3f61686,V_3f61682),G),s(V_3f61686,X))) => s(fun(V_3f61686,V_3f61682),F) = s(fun(V_3f61686,V_3f61682),G))).
fof('h4/thm/pair/pair_case_cong_', conjecture, ![B,C,A]: ![V_27f_5c_27_27, M, V_27M_5c_27_27, F]: ((s('h4/type/pair/prod'(B,C),M) = s('h4/type/pair/prod'(B,C),V_27M_5c_27_27) & ![X, Y]: (s('h4/type/pair/prod'(B,C),V_27M_5c_27_27) = s('h4/type/pair/prod'(B,C),'h4/const/pair/,'(s(B,X),s(C,Y))) => s(A,happ(s(fun(C,A),happ(s(fun(B,fun(C,A)),F),s(B,X))),s(C,Y))) = s(A,happ(s(fun(C,A),happ(s(fun(B,fun(C,A)),V_27f_5c_27_27),s(B,X))),s(C,Y))))) => s(A,'h4/const/pair/pair_CASE'(s('h4/type/pair/prod'(B,C),M),s(fun(B,fun(C,A)),F))) = s(A,'h4/const/pair/pair_CASE'(s('h4/type/pair/prod'(B,C),V_27M_5c_27_27),s(fun(B,fun(C,A)),V_27f_5c_27_27))))).
