Theorems · Theorem · functional analysis
setOfPred_gauge_le_eq
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {a : ℝ},
Convex ℝ s → 0 ∈ s → Absorbent ℝ s → 0 ≤ a → {x | gauge s x ≤ a} = ⋂ r, ⋂ (_ : a < r), r • s- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement and proof · cited by 6,101
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Set.extproof · cited by 2,266
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
Cited by3
Results whose statement or proof uses this declaration.
- Convex.setOfPred_gauge_leproof · cited by 2
- gauge_le_eqproof · cited by 0
- setOf_gauge_le_eqproof · cited by 0