%   ORIGINAL: 'h4/thm/real/REAL_MIN_LE_'
% 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: !z x y. 'h4/const/real/real_lte' ('h4/const/real/min' x y) z <=> 'h4/const/real/real_lte' x z \/ 'h4/const/real/real_lte' y z
%   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: !z x y. 'h4/const/real/real_lte' ('h4/const/real/min' x y) z <=> 'h4/const/real/real_lte' x z \/ 'h4/const/real/real_lte' y z
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_3f95920,V_3f95916]: ![F, G]: (![X]: s(V_3f95916,happ(s(fun(V_3f95920,V_3f95916),F),s(V_3f95920,X))) = s(V_3f95916,happ(s(fun(V_3f95920,V_3f95916),G),s(V_3f95920,X))) => s(fun(V_3f95920,V_3f95916),F) = s(fun(V_3f95920,V_3f95916),G))).
fof('h4/thm/real/REAL_MIN_LE_', conjecture, ![Z, X, Y]: (p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/real/min'(s('h4/type/realax/real',X),s('h4/type/realax/real',Y))),s('h4/type/realax/real',Z)))) <=> (p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',X),s('h4/type/realax/real',Z)))) | p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',Y),s('h4/type/realax/real',Z))))))).
