Theorems · Theorem · general topology
unitInterval.mul_pos_mem_iff
∀ {a t : ℝ}, 0 < a → (a * t ∈ unitInterval ↔ t ∈ Set.Icc 0 (1 / a))- Defined in
- Mathlib.Topology.UnitInterval
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- Set.Iccstatement and proof · cited by 1,702
- unitIntervalstatement and proof · cited by 607
- mul_nonnegproof · cited by 397
- le_div_iff₀proof · cited by 75
- nonneg_of_mul_nonneg_rightproof · cited by 8
Cited by17
Results whose statement or proof uses this declaration.
- Path.trans_applystatement and proof · cited by 9
- Path.trans_symmproof · cited by 3
- Path.extend_trans_of_le_halfproof · cited by 3
- ContinuousMap.Homotopy.symm_transproof · cited by 3
- ContinuousMap.Homotopy.trans_applystatement and proof · cited by 3
- IsLocalHomeomorph.existsUnique_continuousMap_liftsproof · cited by 2
- unitInterval.qRight_zero_rightproof · cited by 1
- Path.delayReflRight_zeroproof · cited by 1
- Path.map_transproof · cited by 1
- IsCoveringMap.liftPath_transproof · cited by 1
- ContinuousMap.HomotopyRel.trans_applystatement · cited by 1
- Path.uniformContinuous_transproof · cited by 0