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Theorems · Theorem · field theory

SubfieldClass.ratCast_mem

∀ {K : Type u} [inst : DivisionRing K] {S : Type u_1} [inst_1 : SetLike S K] [h : SubfieldClass S K] (s : S) (q : ℚ),
  ↑q ∈ s
Defined in
Mathlib.Algebra.Field.Subfield.Defs
Cited by
2 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRingSetLikeSubfieldClass
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Around this declaration

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

Real.subfield_eq_of_closed · cited by 1Real.subfield_eq_of_closedSubfieldClass.qsmul_mem · cited by 0SubfieldClass.qsmul_memSetLike · cited by 1084SetLikeDivisionRing · cited by 1062DivisionRingRat.cast_def · cited by 20Rat.cast_defdiv_mem · cited by 9div_memSubfieldClass · cited by 9SubfieldClassintCast_mem · cited by 7intCast_memnatCast_mem · cited by 6natCast_memSubfieldClass.ratCast_memCITED 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.