%   ORIGINAL: 'h4/thm/combin/GEN_literal_case_RAND_'
% 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 P. P ('h4/const/bool/literal_case' f v) = 'h4/const/bool/literal_case' ('h4/const/combin/o' P f) v
%   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 P. happ P ('h4/const/bool/literal_case' f v) = 'h4/const/bool/literal_case' ('h4/const/combin/o' P f) v
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_3f39006,V_3f39002]: ![F, G]: (![X]: s(V_3f39002,happ(s(fun(V_3f39006,V_3f39002),F),s(V_3f39006,X))) = s(V_3f39002,happ(s(fun(V_3f39006,V_3f39002),G),s(V_3f39006,X))) => s(fun(V_3f39006,V_3f39002),F) = s(fun(V_3f39006,V_3f39002),G))).
fof('h4/thm/combin/GEN_literal_case_RAND_', conjecture, ![A,B,C]: ![V, F, P]: s(A,happ(s(fun(B,A),P),s(B,'h4/const/bool/literal_case'(s(fun(C,B),F),s(C,V))))) = s(A,'h4/const/bool/literal_case'(s(fun(C,A),'h4/const/combin/o'(s(fun(B,A),P),s(fun(C,B),F))),s(C,V)))).
