%   ORIGINAL: 'h4/thm/sum/sum_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: !'f1\'' 'f\'' M 'M\'' f f1. M = 'M\'' /\ (!x. 'M\'' = 'h4/const/sum/INL' x ==> f x = 'f\'' x) /\ (!y. 'M\'' = 'h4/const/sum/INR' y ==> f1 y = 'f1\'' y) ==> 'h4/const/sum/sum_CASE' M f f1 = 'h4/const/sum/sum_CASE' 'M\'' 'f\'' 'f1\''
%   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: !'f1\'' 'f\'' M 'M\'' f f1. M = 'M\'' /\ (!x. 'M\'' = 'h4/const/sum/INL' x ==> happ f x = happ 'f\'' x) /\ (!y. 'M\'' = 'h4/const/sum/INR' y ==> happ f1 y = happ 'f1\'' y) ==> 'h4/const/sum/sum_CASE' M f f1 = 'h4/const/sum/sum_CASE' 'M\'' 'f\'' 'f1\''
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_3f66386,V_3f66382]: ![F, G]: (![X]: s(V_3f66382,happ(s(fun(V_3f66386,V_3f66382),F),s(V_3f66386,X))) = s(V_3f66382,happ(s(fun(V_3f66386,V_3f66382),G),s(V_3f66386,X))) => s(fun(V_3f66386,V_3f66382),F) = s(fun(V_3f66386,V_3f66382),G))).
fof('h4/thm/sum/sum_case_cong_', conjecture, ![A,B,C]: ![V_27f1_5c_27_27, V_27f_5c_27_27, M, V_27M_5c_27_27, F, F1]: ((s('h4/type/sum/sum'(A,B),M) = s('h4/type/sum/sum'(A,B),V_27M_5c_27_27) & (![X]: (s('h4/type/sum/sum'(A,B),V_27M_5c_27_27) = s('h4/type/sum/sum'(A,B),'h4/const/sum/INL'(s(A,X))) => s(C,happ(s(fun(A,C),F),s(A,X))) = s(C,happ(s(fun(A,C),V_27f_5c_27_27),s(A,X)))) & ![Y]: (s('h4/type/sum/sum'(A,B),V_27M_5c_27_27) = s('h4/type/sum/sum'(A,B),'h4/const/sum/INR'(s(B,Y))) => s(C,happ(s(fun(B,C),F1),s(B,Y))) = s(C,happ(s(fun(B,C),V_27f1_5c_27_27),s(B,Y)))))) => s(C,'h4/const/sum/sum_CASE'(s('h4/type/sum/sum'(A,B),M),s(fun(A,C),F),s(fun(B,C),F1))) = s(C,'h4/const/sum/sum_CASE'(s('h4/type/sum/sum'(A,B),V_27M_5c_27_27),s(fun(A,C),V_27f_5c_27_27),s(fun(B,C),V_27f1_5c_27_27))))).
