%   ORIGINAL: 'h4/thm/ind_type/ZRECSPACE_strongind_'
% 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: !'ZRECSPACE\''. 'ZRECSPACE\'' 'h4/const/ind_type/ZBOT' /\ (!c i r. (!n. 'h4/const/ind_type/ZRECSPACE' (r n) /\ 'ZRECSPACE\'' (r n)) ==> 'ZRECSPACE\'' ('h4/const/ind_type/ZCONSTR' c i r)) ==> (!a0. 'h4/const/ind_type/ZRECSPACE' a0 ==> 'ZRECSPACE\'' a0)
%   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: !'ZRECSPACE\''. happ 'ZRECSPACE\'' 'h4/const/ind_type/ZBOT' /\ (!c i r. (!n. 'h4/const/ind_type/ZRECSPACE' (happ r n) /\ happ 'ZRECSPACE\'' (happ r n)) ==> happ 'ZRECSPACE\'' ('h4/const/ind_type/ZCONSTR' c i r)) ==> (!a0. 'h4/const/ind_type/ZRECSPACE' a0 ==> happ 'ZRECSPACE\'' a0)
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_3f74089,V_3f74085]: ![F, G]: (![X]: s(V_3f74085,happ(s(fun(V_3f74089,V_3f74085),F),s(V_3f74089,X))) = s(V_3f74085,happ(s(fun(V_3f74089,V_3f74085),G),s(V_3f74089,X))) => s(fun(V_3f74089,V_3f74085),F) = s(fun(V_3f74089,V_3f74085),G))).
fof('h4/thm/ind_type/ZRECSPACE_strongind_', conjecture, ![A]: ![V_27ZRECSPACE_5c_27_27]: ((p(s(bool,happ(s(fun(fun('h4/type/num/num',fun(A,bool)),bool),V_27ZRECSPACE_5c_27_27),s(fun('h4/type/num/num',fun(A,bool)),'h4/const/ind_type/ZBOT')))) & ![C, I, R]: (![N]: (p(s(bool,'h4/const/ind_type/ZRECSPACE'(s(fun('h4/type/num/num',fun(A,bool)),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,bool))),R),s('h4/type/num/num',N)))))) & p(s(bool,happ(s(fun(fun('h4/type/num/num',fun(A,bool)),bool),V_27ZRECSPACE_5c_27_27),s(fun('h4/type/num/num',fun(A,bool)),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,bool))),R),s('h4/type/num/num',N))))))) => p(s(bool,happ(s(fun(fun('h4/type/num/num',fun(A,bool)),bool),V_27ZRECSPACE_5c_27_27),s(fun('h4/type/num/num',fun(A,bool)),'h4/const/ind_type/ZCONSTR'(s('h4/type/num/num',C),s(A,I),s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,bool))),R)))))))) => ![A0]: (p(s(bool,'h4/const/ind_type/ZRECSPACE'(s(fun('h4/type/num/num',fun(A,bool)),A0)))) => p(s(bool,happ(s(fun(fun('h4/type/num/num',fun(A,bool)),bool),V_27ZRECSPACE_5c_27_27),s(fun('h4/type/num/num',fun(A,bool)),A0))))))).
