Theorems · Definition · field theory
RatFunc.inftyValuation
(F : Type u_1) → [inst : Field F] → [DecidableEq (RatFunc F)] → Valuation (RatFunc F) (WithZero (Multiplicative ℤ))
The valuation at infinity on F(t).
- Defined in
- Mathlib.FieldTheory.RatFunc.Valuation
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- WithZerostatement · cited by 586
- RatFuncstatement and proof · cited by 301
- RatFunc.inftyValuationDefproof · cited by 17
- RatFunc.InftyValuation.map_add_le_max'proof · cited by 1
- RatFunc.InftyValuation.map_mul'proof · cited by 1
- RatFunc.InftyValuation.map_one'proof · cited by 1
- RatFunc.InftyValuation.map_zero'proof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- RatFunc.inftyValuedproof · cited by 4
- RatFunc.inftyValuation.Xstatement · cited by 4
- RatFunc.adicValuation_not_isEquiv_infty_valuationstatement and proof · cited by 2
- RatFunc.inftyValuation.X_zpowstatement and proof · cited by 2
- RatFunc.valuation_isEquiv_inftyValuation_of_one_lt_valuation_Xstatement and proof · cited by 1
- RatFunc.valuation_isEquiv_infty_or_adicstatement and proof · cited by 1
- RatFunc.inftyValuation_applystatement · cited by 1
- RatFunc.inftyValuation.Cstatement · cited by 1
- RatFunc.inftyValuation.X_invstatement and proof · cited by 1
- FunctionField.inftyValuation.Xstatement · cited by 0
- FunctionField.inftyValuation.X_invstatement · cited by 0
- FunctionField.inftyValuation.X_zpowstatement · cited by 0