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Theorems · Theorem · commutative algebra

Field.gcd_eq

∀ {K : Type u_1} [inst : Field K] [inst_1 : DecidableEq K] (a b : K), EuclideanDomain.gcd a b = if a = 0 then b else a
Defined in
Mathlib.Algebra.EuclideanDomain.Field
Cited by
2 results in Mathlib
Foundations
Depth 48 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.

Field.gcd_eq_of_ne · cited by 0Field.gcd_eq_of_neField.gcd_zero_eq · cited by 0Field.gcd_zero_eqField · cited by 7404Fieldsub_self · cited by 996sub_selfmul_div_cancel_right₀ · cited by 70mul_div_cancel_right₀EuclideanDomain.gcd · cited by 39EuclideanDomain.gcdEuclideanDomain.gcd_zero_left · cited by 7EuclideanDomain.gcd_zero_…EuclideanDomain.gcd.eq_def · cited by 1gcd.eq_defField.gcd_eqCITED BYCITES

Cites6

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.