mathlib documentation

tactic.omega.int.preterm

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meta inductive omega.int.exprterm  :
Type

The shadow syntax for arithmetic terms. All constants are reified to cst (e.g., -5 is reified to cst -5) and all other atomic terms are reified to exp (e.g., -5 * (gcd 14 -7) is reified to exp -5 \(gcd 14 -7)).expaccepts a coefficient of typeint` as its first argument because multiplication by constant is allowed by the omega test.

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@[protected, instance]
meta def omega.int.preterm.has_reflect  :
has_reflect omega.int.preterm
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@[protected, instance]
def omega.int.preterm.inhabited  :
inhabited omega.int.preterm
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inductive omega.int.preterm  :
Type

Similar to exprterm, except that all exprs are now replaced with de Brujin indices of type nat. This is akin to generalizing over the terms represented by the said exprs.

Instances for omega.int.preterm
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@[simp]
def omega.int.preterm.val (v : ℕ → ℤ) :
omega.int.preterm → ℤ

Preterm evaluation

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def omega.int.preterm.fresh_index  :
omega.int.preterm → ℕ

Fresh de Brujin index not used by any variable in argument

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@[simp]
def omega.int.preterm.add_one (t : omega.int.preterm) :
omega.int.preterm
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def omega.int.preterm.repr  :
omega.int.preterm → string
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@[simp]
def omega.int.canonize  :
omega.int.preterm → omega.term

Return a term (which is in canonical form by definition) that is equivalent to the input preterm

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@[simp]
theorem omega.int.val_canonize {v : ℕ → ℤ} {t : omega.int.preterm} :
omega.term.val v (omega.int.canonize t) = omega.int.preterm.val v t