Library Coq.Num.NeqAxioms

InEquality is introduced as an independant parameter, it could be instantiated with the negation of equality





Require Export EqParams.

Require Export NeqParams.




Axiom eq_not_neq : (x,y:N)x=y->~(x<>y).

Hints Immediate eq_not_neq : num.




Axiom neq_sym : (x,y:N)(x<>y)->(y<>x).

Hints Resolve neq_sym : num.




Axiom neq_not_neq_trans : (x,y,z:N)(x<>y)->~(y<>z)->(x<>z).

Hints Resolve neq_not_neq_trans : num.