%   ORIGINAL: 'h4/thm/numpair/ncons_11_'
% 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: !y x t h. 'h4/const/numpair/ncons' x y = 'h4/const/numpair/ncons' h t <=> x = h /\ y = t
%   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: !y x t h. 'h4/const/numpair/ncons' x y = 'h4/const/numpair/ncons' h t <=> x = h /\ y = t
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_3f62936,V_3f62932]: ![F, G]: (![X]: s(V_3f62932,happ(s(fun(V_3f62936,V_3f62932),F),s(V_3f62936,X))) = s(V_3f62932,happ(s(fun(V_3f62936,V_3f62932),G),s(V_3f62936,X))) => s(fun(V_3f62936,V_3f62932),F) = s(fun(V_3f62936,V_3f62932),G))).
fof('h4/thm/numpair/ncons_11_', conjecture, ![Y, X, T, H]: (s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',X),s('h4/type/num/num',Y))) = s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',H),s('h4/type/num/num',T))) <=> (s('h4/type/num/num',X) = s('h4/type/num/num',H) & s('h4/type/num/num',Y) = s('h4/type/num/num',T)))).
