Library Coq.Num.NeqDef

DisEquality is defined as the negation of equality





Require Params.

Require EqParams.

Require EqAxioms.




Definition neq : N -> N -> Prop := [x,y] ~(x=y).

Infix 6 "<>" neq V8only 70.




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

Unfold neq; Auto with num.

Qed.

Hints Immediate eq_not_neq : num.




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

Unfold neq; Auto with num.

Qed.

Hints Resolve neq_sym : num.




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

Unfold neq; EAuto with num.

Qed.

Hints Resolve neq_not_neq_trans : num.