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Theorems · Theorem · order theory

one_le_pow_iff

∀ {M : Type u_3} [inst : Monoid M] [inst_1 : LinearOrder M] [MulLeftMono M] {x : M} {n : ℕ}, n ≠ 0 → (1 ≤ x ^ n ↔ 1 ≤ x)
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Pow
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
MonoidLinearOrderMulLeftMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

pow_le_one_iff · cited by 1pow_le_one_iffpow_lt_one_iff · cited by 1pow_lt_one_iffLinearOrder · cited by 8572LinearOrderMonoid · cited by 3887MonoidMulLeftMono · cited by 410MulLeftMonoone_le_pow_of_one_le' · cited by 6one_le_pow_of_one_le'le_imp_le_of_lt_imp_lt · cited by 3le_imp_le_of_lt_imp_ltpow_lt_one' · cited by 2pow_lt_one'one_le_pow_iffCITED BYCITES

Cites6

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Cited by2

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