Theorems · Theorem · commutative algebra
contraction_of_isPowMul
∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedRing α] [inst_1 : SeminormedRing β],
IsPowMul norm → ∀ {f : α →+* β}, f.IsBounded → ∀ (x : α), ‖f x‖ ≤ ‖x‖Given a bounded f : α →+* β between seminormed rings, is the seminorm on β is
power-multiplicative, then f is a contraction.
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- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingSeminormedRing
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- RingHomstatement and proof · cited by 10,189
- Norm.normstatement and proof · cited by 5,413
- SeminormedRingstatement and proof · cited by 446
- IsPowMulstatement and proof · cited by 39
- SeminormedRing.toRingSeminormproof · cited by 10
- contraction_of_isPowMul_of_boundedWrtproof · cited by 2
- RingHom.IsBoundedstatement and proof · cited by 1
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