Library Coq.Num.EqAxioms

Axioms for equality


Require Export Params.

Require Export EqParams.

Require Export NSyntax.

Basic Axioms for eq





Axiom eq_refl : (x:N)(x=x).

Axiom eq_sym : (x,y:N)(x=y)->(y=x).

Axiom eq_trans : (x,y,z:N)(x=y)->(y=z)->(x=z).

Axioms for eq and add


Axiom add_eq_compat : (x1,x2,y1,y2:N)(x1=x2)->(y1=y2)->(x1+y1)=(x2+y2).

Axioms for eq and S


Axiom S_eq_compat : (x,y:N)(x=y)->(S x)=(S y).

Axioms for eq and <


Axiom lt_eq_compat : (x1,x2,y1,y2:N)(x1=y1)->(x2=y2)->(x1<x2)->(y1<y2).




Hints Resolve eq_refl eq_trans add_eq_compat S_eq_compat lt_eq_compat : num.

Hints Immediate eq_sym : num.