%   ORIGINAL: 'h4/thm/while/OWHILE_INV_IND_'
% 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: !P G f s. P s /\ (!x. P x /\ G x ==> P (f x)) ==> (!'s\''. 'h4/const/while/OWHILE' G f s = 'h4/const/option/SOME' 's\'' ==> P 's\'')
%   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: !P G f s. happ P s /\ (!x. happ P x /\ happ G x ==> happ P (happ f x)) ==> (!'s\''. 'h4/const/while/OWHILE' G f s = 'h4/const/option/SOME' 's\'' ==> happ P 's\'')
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_3f41884,V_3f41880]: ![F, G]: (![X]: s(V_3f41880,happ(s(fun(V_3f41884,V_3f41880),F),s(V_3f41884,X))) = s(V_3f41880,happ(s(fun(V_3f41884,V_3f41880),G),s(V_3f41884,X))) => s(fun(V_3f41884,V_3f41880),F) = s(fun(V_3f41884,V_3f41880),G))).
fof('h4/thm/while/OWHILE_INV_IND_', conjecture, ![A]: ![P, G, F, S]: ((p(s(bool,happ(s(fun(A,bool),P),s(A,S)))) & ![X]: ((p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) & p(s(bool,happ(s(fun(A,bool),G),s(A,X))))) => p(s(bool,happ(s(fun(A,bool),P),s(A,happ(s(fun(A,A),F),s(A,X)))))))) => ![V_27s_5c_27_27]: (s('h4/type/option/option'(A),'h4/const/while/OWHILE'(s(fun(A,bool),G),s(fun(A,A),F),s(A,S))) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,V_27s_5c_27_27))) => p(s(bool,happ(s(fun(A,bool),P),s(A,V_27s_5c_27_27))))))).
