%   ORIGINAL: 'h4/thm/arithmetic/MODEQ_MULT_CONG_'
% 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: !y1 y0 x1 x0 n. 'h4/const/arithmetic/MODEQ' n x0 x1 ==> 'h4/const/arithmetic/MODEQ' n y0 y1 ==> 'h4/const/arithmetic/MODEQ' n ('h4/const/arithmetic/*' x0 y0) ('h4/const/arithmetic/*' x1 y1)
%   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: !y1 y0 x1 x0 n. 'h4/const/arithmetic/MODEQ' n x0 x1 ==> 'h4/const/arithmetic/MODEQ' n y0 y1 ==> 'h4/const/arithmetic/MODEQ' n ('h4/const/arithmetic/*' x0 y0) ('h4/const/arithmetic/*' x1 y1)
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_3f86019,V_3f86015]: ![F, G]: (![X]: s(V_3f86015,happ(s(fun(V_3f86019,V_3f86015),F),s(V_3f86019,X))) = s(V_3f86015,happ(s(fun(V_3f86019,V_3f86015),G),s(V_3f86019,X))) => s(fun(V_3f86019,V_3f86015),F) = s(fun(V_3f86019,V_3f86015),G))).
fof('h4/thm/arithmetic/MODEQ_MULT_CONG_', conjecture, ![Y1, Y0, X1, X0, N]: (p(s(bool,'h4/const/arithmetic/MODEQ'(s('h4/type/num/num',N),s('h4/type/num/num',X0),s('h4/type/num/num',X1)))) => (p(s(bool,'h4/const/arithmetic/MODEQ'(s('h4/type/num/num',N),s('h4/type/num/num',Y0),s('h4/type/num/num',Y1)))) => p(s(bool,'h4/const/arithmetic/MODEQ'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num',X0),s('h4/type/num/num',Y0))),s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num',X1),s('h4/type/num/num',Y1))))))))).
