%   ORIGINAL: 'h4/thm/list/MAP2_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: !l1 'l1\'' l2 'l2\'' f 'f\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 'l2\'') ==> f x y = 'f\'' x y) ==> 'h4/const/list/MAP2' f l1 l2 = 'h4/const/list/MAP2' 'f\'' 'l1\'' 'l2\''
%   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: !l1 'l1\'' l2 'l2\'' f 'f\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 'l2\'') ==> happ (happ f x) y = happ (happ 'f\'' x) y) ==> 'h4/const/list/MAP2' f l1 l2 = 'h4/const/list/MAP2' 'f\'' 'l1\'' 'l2\''
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_3f6064,V_3f6060]: ![F, G]: (![X]: s(V_3f6060,happ(s(fun(V_3f6064,V_3f6060),F),s(V_3f6064,X))) = s(V_3f6060,happ(s(fun(V_3f6064,V_3f6060),G),s(V_3f6064,X))) => s(fun(V_3f6064,V_3f6060),F) = s(fun(V_3f6064,V_3f6060),G))).
fof('h4/thm/list/MAP2_CONG_', conjecture, ![C,A,B]: ![L1, V_27l1_5c_27_27, L2, V_27l2_5c_27_27, F, V_27f_5c_27_27]: ((s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),V_27l1_5c_27_27) & (s('h4/type/list/list'(B),L2) = s('h4/type/list/list'(B),V_27l2_5c_27_27) & ![X, Y]: ((p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),V_27l1_5c_27_27)))))) & p(s(bool,'h4/const/bool/IN'(s(B,Y),s(fun(B,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(B),V_27l2_5c_27_27))))))) => s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F),s(A,X))),s(B,Y))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),V_27f_5c_27_27),s(A,X))),s(B,Y)))))) => s('h4/type/list/list'(C),'h4/const/list/MAP2'(s(fun(A,fun(B,C)),F),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))) = s('h4/type/list/list'(C),'h4/const/list/MAP2'(s(fun(A,fun(B,C)),V_27f_5c_27_27),s('h4/type/list/list'(A),V_27l1_5c_27_27),s('h4/type/list/list'(B),V_27l2_5c_27_27))))).
