%   ORIGINAL: 'h4/thm/bool/SWAP_FORALL_THM_'
% 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. (!x y. P x y) <=> (!y x. P x y)
%   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. (!x y. happ (happ P x) y) <=> (!y x. happ (happ P x) y)
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_3f34278,V_3f34274]: ![F, G]: (![X]: s(V_3f34274,happ(s(fun(V_3f34278,V_3f34274),F),s(V_3f34278,X))) = s(V_3f34274,happ(s(fun(V_3f34278,V_3f34274),G),s(V_3f34278,X))) => s(fun(V_3f34278,V_3f34274),F) = s(fun(V_3f34278,V_3f34274),G))).
fof('h4/thm/bool/SWAP_FORALL_THM_', conjecture, ![A,B]: ![P]: (![X, Y]: p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,X))),s(B,Y)))) <=> ![Y, X]: p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,X))),s(B,Y)))))).
