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Theorems · Theorem · commutative algebra

invOf_le_one

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],
  1 ≤ a → ⅟a ≤ 1
Defined in
Mathlib.Algebra.Order.Invertible
Cited by
1 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringLinearOrderIsStrictOrderedRingInvertible
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Around this declaration

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

midpoint_le_midpoint · cited by 2midpoint_le_midpointSemiring · cited by 13802SemiringLinearOrder · cited by 8572LinearOrderLE.le.trans · cited by 3151le.transIsStrictOrderedRing · cited by 2490IsStrictOrderedRingInvertible · cited by 549Invertiblezero_le_one · cited by 316zero_le_oneInvertible.invOf · cited by 268Invertible.invOfmul_invOf_self · cited by 28mul_invOf_selfle_mul_of_one_le_left · cited by 19le_mul_of_one_le_leftinvOf_nonneg · cited by 2invOf_nonneginvOf_le_oneCITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.