%   ORIGINAL: 'h4/thm/ind_type/CONSTR_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. P 'h4/const/ind_type/BOTTOM' /\ (!c i r. (!n. P (r n)) ==> P ('h4/const/ind_type/CONSTR' c i r)) ==> (!x. P 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: !P. happ P 'h4/const/ind_type/BOTTOM' /\ (!c i r. (!n. happ P (happ r n)) ==> happ P ('h4/const/ind_type/CONSTR' c i r)) ==> (!x. happ P 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_3f74239,V_3f74235]: ![F, G]: (![X]: s(V_3f74235,happ(s(fun(V_3f74239,V_3f74235),F),s(V_3f74239,X))) = s(V_3f74235,happ(s(fun(V_3f74239,V_3f74235),G),s(V_3f74239,X))) => s(fun(V_3f74239,V_3f74235),F) = s(fun(V_3f74239,V_3f74235),G))).
fof('h4/thm/ind_type/CONSTR_IND_', conjecture, ![A]: ![P]: ((p(s(bool,happ(s(fun('h4/type/ind_type/recspace'(A),bool),P),s('h4/type/ind_type/recspace'(A),'h4/const/ind_type/BOTTOM')))) & ![C, I, R]: (![N]: p(s(bool,happ(s(fun('h4/type/ind_type/recspace'(A),bool),P),s('h4/type/ind_type/recspace'(A),happ(s(fun('h4/type/num/num','h4/type/ind_type/recspace'(A)),R),s('h4/type/num/num',N)))))) => p(s(bool,happ(s(fun('h4/type/ind_type/recspace'(A),bool),P),s('h4/type/ind_type/recspace'(A),'h4/const/ind_type/CONSTR'(s('h4/type/num/num',C),s(A,I),s(fun('h4/type/num/num','h4/type/ind_type/recspace'(A)),R)))))))) => ![X]: p(s(bool,happ(s(fun('h4/type/ind_type/recspace'(A),bool),P),s('h4/type/ind_type/recspace'(A),X)))))).
