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.
Lemma
eq_not_neq : (x,y:N)x=y->~(x<>y).
Unfold neq; Auto with num.
Save
.
Hints
Immediate
eq_not_neq : num.
Lemma
neq_sym : (x,y:N)(x<>y)->(y<>x).
Unfold neq; Auto with num.
Save
.
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.
Save
.
Hints
Resolve neq_not_neq_trans : num.