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Theorems · Theorem · commutative algebra

Subring.pow_mem

∀ {R : Type u_1} [inst : Ring R] (s : Subring R) {x : R}, x ∈ s → ∀ (n : ℕ), x ^ n ∈ s
Defined in
Mathlib.Algebra.Ring.Subring.Defs
Cited by
1 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext
Assumes
Ring

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Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Ringstatement and proof · cited by 7,463
  • Subringstatement and proof · cited by 602
  • pow_memproof · cited by 46

Cited by1

Results whose statement or proof uses this declaration.