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Theorems · Theorem · field theory

Rat.cast_commute

∀ {α : Type u_3} [inst : DivisionRing α] (r : ℚ) (a : α), Commute (↑r) a
Defined in
Mathlib.Data.Rat.Cast.Defs
Cited by
2 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRing
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Around this declaration

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

Rat.commute_cast · cited by 0Rat.commute_castRat.cast_comm · cited by 0Rat.cast_commDivisionRing · cited by 1062DivisionRingCommute · cited by 639CommuteNat.cast_commute · cited by 24Nat.cast_commuteRat.cast_def · cited by 20Rat.cast_defInt.cast_commute · cited by 7Int.cast_commuteCommute.div_left · cited by 2Commute.div_leftRat.cast_commuteCITED 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.