Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono
∀ {R : Type u_2} {Γ : Type u_3} [inst : Ring R] [inst_1 : ValuativeRel R] [inst_2 : LinearOrderedCommGroupWithZero Γ]
(v : Valuation R Γ) [inst_3 : v.Compatible], StrictMono ⇑(ValuativeRel.ValueGroupWithZero.orderMonoidIso v)The map orderMonoidIso v is strictly monotone.
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- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- Valuationstatement and proof · cited by 823
- StrictMonostatement · cited by 706
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- ValuativeRelstatement and proof · cited by 241
- MonoidWithZeroHom.ofClassstatement · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement · cited by 166
- OrderMonoidIsostatement · cited by 114
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