mathlib documentation

tactic.omega.nat.form

@[simp]
def omega.nat.univ_close (p : omega.nat.preform) :
() → Prop

univ_close p n := p closed by prepending n universal quantifiers

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Return expr of proof that argument is free of subtractions

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theorem omega.nat.preform.holds_constant {v w : } (p : omega.nat.preform) :
(∀ (x : ), x < p.fresh_indexv x = w x)(omega.nat.preform.holds v p omega.nat.preform.holds w p)

All valuations satisfy argument

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There exists some valuation that satisfies argument

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implies p q := under any valuation, q holds if p holds

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equiv p q := under any valuation, p holds iff q holds

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There does not exist any valuation that satisfies argument

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Tactic for setting up proof by induction over preforms.