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Theorems · Theorem · order theory

one_lt_zpow

∀ {G : Type u_2} [inst : DivInvMonoid G] [inst_1 : Preorder G] [MulLeftMono G] {x : G},
  1 < x → ∀ {n : ℤ}, 0 < n → 1 < x ^ n
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Pow
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext
Assumes
DivInvMonoidPreorderMulLeftMono
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Around this declaration

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

zpow_left_strictMono · cited by 3zpow_left_strictMonoPreorder · cited by 7952PreorderLT.lt.ne' · cited by 1417lt.ne'MulLeftMono · cited by 410MulLeftMonozpow_natCast · cited by 271zpow_natCastDivInvMonoid · cited by 103DivInvMonoidone_lt_pow' · cited by 2one_lt_pow'one_lt_zpowCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.