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Theorems · Theorem · field theory

RatFunc.inftyValuation_of_nonzero

∀ (F : Type u_1) [inst : Field F] [inst_1 : DecidableEq (RatFunc F)] {x : RatFunc F},
  x ≠ 0 → RatFunc.inftyValuationDef F x = WithZero.exp x.intDegree
Defined in
Mathlib.FieldTheory.RatFunc.Valuation
Cited by
2 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RatFunc.inftyValuation.C · cited by 1inftyValuation.CFunctionField.inftyValuation_of_nonzero · cited by 0FunctionField.inftyValuat…Field · cited by 7404FieldMultiplicative · cited by 875MultiplicativeWithZero · cited by 586WithZeroRatFunc · cited by 301RatFuncWithZero.exp · cited by 112WithZero.expRatFunc.intDegree · cited by 18RatFunc.intDegreeRatFunc.inftyValuationDef · cited by 17RatFunc.inftyValuationDefRatFunc.inftyValuation_of_non…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.