instNoZeroSMulDivisorsSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers

English

The module structure on the adicCompletionIntegers K v has the NoZeroSMulDivisors property relative to R; i.e., if r ≠ 0 and r • x = 0 then x = 0 for x in the subtype adicCompletionIntegers.

Русский

У модуля над R на adicCompletionIntegers K v свойство NoZeroSMulDivisors: если r ≠ 0 и r•x = 0, то x = 0.

LaTeX

$$NoZeroSMulDivisors R (v.adicCompletionIntegers K)$$

Lean4

instance : NoZeroSMulDivisors R (v.adicCompletionIntegers K) where eq_zero_or_eq_zero_of_smul_eq_zero {c x} := by simp

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