%   ORIGINAL: 'h4/thm/option/option_CLAUSES_12'
% 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: !f e x. 'h4/const/option/IS_SOME' x ==> 'h4/const/option/option_CASE' x e f = f ('h4/const/option/THE' x)
%   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: !f e x. 'h4/const/option/IS_SOME' x ==> 'h4/const/option/option_CASE' x e f = happ f ('h4/const/option/THE' x)
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_3f99707,V_3f99703]: ![F, G]: (![X]: s(V_3f99703,happ(s(fun(V_3f99707,V_3f99703),F),s(V_3f99707,X))) = s(V_3f99703,happ(s(fun(V_3f99707,V_3f99703),G),s(V_3f99707,X))) => s(fun(V_3f99707,V_3f99703),F) = s(fun(V_3f99707,V_3f99703),G))).
fof('h4/thm/option/option_CLAUSES_12', conjecture, ![B,A]: ![F, E, X]: (p(s(bool,'h4/const/option/IS_SOME'(s('h4/type/option/option'(A),X)))) => s(B,'h4/const/option/option_CASE'(s('h4/type/option/option'(A),X),s(B,E),s(fun(A,B),F))) = s(B,happ(s(fun(A,B),F),s(A,'h4/const/option/THE'(s('h4/type/option/option'(A),X))))))).
