%   ORIGINAL: 'h4/thm/ind_type/INJP_INJ_'
% 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: !f1 'f1\'' f2 'f2\''. 'h4/const/ind_type/INJP' f1 f2 = 'h4/const/ind_type/INJP' 'f1\'' 'f2\'' <=> f1 = 'f1\'' /\ f2 = 'f2\''
%   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: !f1 'f1\'' f2 'f2\''. 'h4/const/ind_type/INJP' f1 f2 = 'h4/const/ind_type/INJP' 'f1\'' 'f2\'' <=> f1 = 'f1\'' /\ f2 = 'f2\''
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_3f73964,V_3f73960]: ![F, G]: (![X]: s(V_3f73960,happ(s(fun(V_3f73964,V_3f73960),F),s(V_3f73964,X))) = s(V_3f73960,happ(s(fun(V_3f73964,V_3f73960),G),s(V_3f73964,X))) => s(fun(V_3f73964,V_3f73960),F) = s(fun(V_3f73964,V_3f73960),G))).
fof('h4/thm/ind_type/INJP_INJ_', conjecture, ![A]: ![F1, V_27f1_5c_27_27, F2, V_27f2_5c_27_27]: (s(fun('h4/type/num/num',fun(A,bool)),'h4/const/ind_type/INJP'(s(fun('h4/type/num/num',fun(A,bool)),F1),s(fun('h4/type/num/num',fun(A,bool)),F2))) = s(fun('h4/type/num/num',fun(A,bool)),'h4/const/ind_type/INJP'(s(fun('h4/type/num/num',fun(A,bool)),V_27f1_5c_27_27),s(fun('h4/type/num/num',fun(A,bool)),V_27f2_5c_27_27))) <=> (s(fun('h4/type/num/num',fun(A,bool)),F1) = s(fun('h4/type/num/num',fun(A,bool)),V_27f1_5c_27_27) & s(fun('h4/type/num/num',fun(A,bool)),F2) = s(fun('h4/type/num/num',fun(A,bool)),V_27f2_5c_27_27)))).
