%   ORIGINAL: 'h4/thm/list/list_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: !'v\'' 'f\'' M 'M\'' v f. M = 'M\'' /\ ('M\'' = 'h4/const/list/NIL' ==> v = 'v\'') /\ (!a0 a1. 'M\'' = 'h4/const/list/CONS' a0 a1 ==> f a0 a1 = 'f\'' a0 a1) ==> 'h4/const/list/list_CASE' M v f = 'h4/const/list/list_CASE' 'M\'' 'v\'' '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: !'v\'' 'f\'' M 'M\'' v f. M = 'M\'' /\ ('M\'' = 'h4/const/list/NIL' ==> v = 'v\'') /\ (!a0 a1. 'M\'' = 'h4/const/list/CONS' a0 a1 ==> happ (happ f a0) a1 = happ (happ 'f\'' a0) a1) ==> 'h4/const/list/list_CASE' M v f = 'h4/const/list/list_CASE' 'M\'' 'v\'' '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_3f2463,V_3f2459]: ![F, G]: (![X]: s(V_3f2459,happ(s(fun(V_3f2463,V_3f2459),F),s(V_3f2463,X))) = s(V_3f2459,happ(s(fun(V_3f2463,V_3f2459),G),s(V_3f2463,X))) => s(fun(V_3f2463,V_3f2459),F) = s(fun(V_3f2463,V_3f2459),G))).
fof('h4/thm/list/list_case_cong_', conjecture, ![A,B]: ![V_27v_5c_27_27, V_27f_5c_27_27, M, V_27M_5c_27_27, V, F]: ((s('h4/type/list/list'(A),M) = s('h4/type/list/list'(A),V_27M_5c_27_27) & ((s('h4/type/list/list'(A),V_27M_5c_27_27) = s('h4/type/list/list'(A),'h4/const/list/NIL') => s(B,V) = s(B,V_27v_5c_27_27)) & ![A0, A1]: (s('h4/type/list/list'(A),V_27M_5c_27_27) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,A0),s('h4/type/list/list'(A),A1))) => s(B,happ(s(fun('h4/type/list/list'(A),B),happ(s(fun(A,fun('h4/type/list/list'(A),B)),F),s(A,A0))),s('h4/type/list/list'(A),A1))) = s(B,happ(s(fun('h4/type/list/list'(A),B),happ(s(fun(A,fun('h4/type/list/list'(A),B)),V_27f_5c_27_27),s(A,A0))),s('h4/type/list/list'(A),A1)))))) => s(B,'h4/const/list/list_CASE'(s('h4/type/list/list'(A),M),s(B,V),s(fun(A,fun('h4/type/list/list'(A),B)),F))) = s(B,'h4/const/list/list_CASE'(s('h4/type/list/list'(A),V_27M_5c_27_27),s(B,V_27v_5c_27_27),s(fun(A,fun('h4/type/list/list'(A),B)),V_27f_5c_27_27))))).
