%   ORIGINAL: 'h4/thm/topology/METRIC_TRIANGLE_'
% 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: !m x y z. 'h4/const/real/real_lte' ('h4/const/topology/dist' m ('h4/const/pair/,' x z)) ('h4/const/realax/real_add' ('h4/const/topology/dist' m ('h4/const/pair/,' x y)) ('h4/const/topology/dist' m ('h4/const/pair/,' 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: !m x y z. 'h4/const/real/real_lte' ('h4/const/topology/dist' m ('h4/const/pair/,' x z)) ('h4/const/realax/real_add' ('h4/const/topology/dist' m ('h4/const/pair/,' x y)) ('h4/const/topology/dist' m ('h4/const/pair/,' 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_3f37805,V_3f37801]: ![F, G]: (![X]: s(V_3f37801,happ(s(fun(V_3f37805,V_3f37801),F),s(V_3f37805,X))) = s(V_3f37801,happ(s(fun(V_3f37805,V_3f37801),G),s(V_3f37805,X))) => s(fun(V_3f37805,V_3f37801),F) = s(fun(V_3f37805,V_3f37801),G))).
fof('h4/thm/topology/METRIC_TRIANGLE_', conjecture, ![A]: ![M, X, Y, Z]: p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/topology/dist'(s('h4/type/topology/metric'(A),M),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,X),s(A,Z))))),s('h4/type/realax/real','h4/const/realax/real_add'(s('h4/type/realax/real','h4/const/topology/dist'(s('h4/type/topology/metric'(A),M),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,X),s(A,Y))))),s('h4/type/realax/real','h4/const/topology/dist'(s('h4/type/topology/metric'(A),M),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,Y),s(A,Z))))))))))).
