Mathlib Map

Theorems · Theorem · commutative algebra

invOf_lt_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
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

midpoint_mem_openSegment · cited by 3midpoint_mem_openSegmentSemiring · cited by 13802SemiringLinearOrder · cited by 8572LinearOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingInvertible · cited by 549InvertibleLT.lt.trans · cited by 370lt.transInvertible.invOf · cited by 268Invertible.invOfone_pos · cited by 102one_posmul_invOf_self · cited by 28mul_invOf_selflt_mul_of_one_lt_left · cited by 5lt_mul_of_one_lt_leftinvOf_pos · cited by 3invOf_posinvOf_lt_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.