Coq.Num.EqAxioms

# Module Coq.Num.EqAxioms

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Axioms for equality

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`Require` `Export` Params.
`Require` `Export` EqParams.
`Require` `Export` NSyntax.

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Basic Axioms for `eq`

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`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).

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Axioms for `eq` and `add`

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

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Axioms for `eq` and `S`

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

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Axioms for `eq` and `<`

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`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.

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Index