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Theorems · Theorem · field theory

Rat.cast_def

∀ {K : Type u_1} [inst : DivisionRing K] (q : ℚ), ↑q = ↑q.num / ↑q.den
Defined in
Mathlib.Algebra.Field.Defs
Cited by
20 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
DivisionRing
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Around this declaration

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

Rat.cast_intCast · cited by 74Rat.cast_intCastRat.cast_neg · cited by 25Rat.cast_negRat.cast_ofNat · cited by 19Rat.cast_ofNatmap_ratCast · cited by 10map_ratCastRat.cast_pow · cited by 7Rat.cast_powRat.cast_divInt_of_ne_zero · cited by 5Rat.cast_divInt_of_ne_zeromap_ratCast_smul · cited by 4map_ratCast_smulLiouvilleWith.mul_rat · cited by 2LiouvilleWith.mul_ratRat.cast_add_of_ne_zero · cited by 2Rat.cast_add_of_ne_zeroRat.cast_commute · cited by 2Rat.cast_commuteSubfieldClass.ratCast_mem · cited by 2SubfieldClass.ratCast_memRat.cast_mul_of_ne_zero · cited by 1Rat.cast_mul_of_ne_zeroRat.cast_nnratCast · cited by 1Rat.cast_nnratCastRat.cast_pos_of_pos · cited by 1Rat.cast_pos_of_posRat.cast_inv_nat · cited by 1Rat.cast_inv_natDivisionRing · cited by 1062DivisionRingDivisionRing.ratCast_def · cited by 1DivisionRing.ratCast_defRat.cast_defCITED BYCITES

Cites2

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

Cited by20

Results whose statement or proof uses this declaration.