%   ORIGINAL: 'h4/thm/list/FOLDL2_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\'' a 'a\'' f 'f\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ a = 'a\'' /\ (!z b c. 'h4/const/bool/IN' b ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' c ('h4/const/list/LIST_TO_SET' 'l2\'') ==> f z b c = 'f\'' z b c) ==> 'h4/const/list/FOLDL2' f a l1 l2 = 'h4/const/list/FOLDL2' 'f\'' 'a\'' '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\'' a 'a\'' f 'f\''. l1 = 'l1\'' /\ l2 = 'l2\'' /\ a = 'a\'' /\ (!z b c. 'h4/const/bool/IN' b ('h4/const/list/LIST_TO_SET' 'l1\'') /\ 'h4/const/bool/IN' c ('h4/const/list/LIST_TO_SET' 'l2\'') ==> happ (happ (happ f z) b) c = happ (happ (happ 'f\'' z) b) c) ==> 'h4/const/list/FOLDL2' f a l1 l2 = 'h4/const/list/FOLDL2' 'f\'' 'a\'' '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_3f7440,V_3f7436]: ![F, G]: (![X]: s(V_3f7436,happ(s(fun(V_3f7440,V_3f7436),F),s(V_3f7440,X))) = s(V_3f7436,happ(s(fun(V_3f7440,V_3f7436),G),s(V_3f7440,X))) => s(fun(V_3f7440,V_3f7436),F) = s(fun(V_3f7440,V_3f7436),G))).
fof('h4/thm/list/FOLDL2_cong_', conjecture, ![C,A,B]: ![L1, V_27l1_5c_27_27, L2, V_27l2_5c_27_27, A0, V_27a_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) & (s(C,A0) = s(C,V_27a_5c_27_27) & ![Z, B0, C0]: ((p(s(bool,'h4/const/bool/IN'(s(A,B0),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,C0),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)),happ(s(fun(C,fun(A,fun(B,C))),F),s(C,Z))),s(A,B0))),s(B,C0))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),happ(s(fun(C,fun(A,fun(B,C))),V_27f_5c_27_27),s(C,Z))),s(A,B0))),s(B,C0))))))) => s(C,'h4/const/list/FOLDL2'(s(fun(C,fun(A,fun(B,C))),F),s(C,A0),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))) = s(C,'h4/const/list/FOLDL2'(s(fun(C,fun(A,fun(B,C))),V_27f_5c_27_27),s(C,V_27a_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))))).
