%   ORIGINAL: 'h4/thm/list/FOLDR_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: !l 'l\'' b 'b\'' f 'f\''. l = 'l\'' /\ b = 'b\'' /\ (!x a. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l\'') ==> f x a = 'f\'' x a) ==> 'h4/const/list/FOLDR' f b l = 'h4/const/list/FOLDR' 'f\'' 'b\'' 'l\''
%   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: !l 'l\'' b 'b\'' f 'f\''. l = 'l\'' /\ b = 'b\'' /\ (!x a. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' 'l\'') ==> happ (happ f x) a = happ (happ 'f\'' x) a) ==> 'h4/const/list/FOLDR' f b l = 'h4/const/list/FOLDR' 'f\'' 'b\'' 'l\''
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_3f5989,V_3f5985]: ![F, G]: (![X]: s(V_3f5985,happ(s(fun(V_3f5989,V_3f5985),F),s(V_3f5989,X))) = s(V_3f5985,happ(s(fun(V_3f5989,V_3f5985),G),s(V_3f5989,X))) => s(fun(V_3f5989,V_3f5985),F) = s(fun(V_3f5989,V_3f5985),G))).
fof('h4/thm/list/FOLDR_CONG_', conjecture, ![B,A]: ![L, V_27l_5c_27_27, B0, V_27b_5c_27_27, F, V_27f_5c_27_27]: ((s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),V_27l_5c_27_27) & (s(B,B0) = s(B,V_27b_5c_27_27) & ![X, A0]: (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_27l_5c_27_27)))))) => s(B,happ(s(fun(B,B),happ(s(fun(A,fun(B,B)),F),s(A,X))),s(B,A0))) = s(B,happ(s(fun(B,B),happ(s(fun(A,fun(B,B)),V_27f_5c_27_27),s(A,X))),s(B,A0)))))) => s(B,'h4/const/list/FOLDR'(s(fun(A,fun(B,B)),F),s(B,B0),s('h4/type/list/list'(A),L))) = s(B,'h4/const/list/FOLDR'(s(fun(A,fun(B,B)),V_27f_5c_27_27),s(B,V_27b_5c_27_27),s('h4/type/list/list'(A),V_27l_5c_27_27))))).
