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Theorems · Theorem · number theory

Rat.cast_pos_of_pos

∀ {q : ℚ} {K : Type u_5} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K], 0 < q → 0 < ↑q
Defined in
Mathlib.Data.Rat.Cast.Order
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRing
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Around this declaration

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

Rat.cast_strictMono · cited by 5Rat.cast_strictMonoLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingdiv_pos · cited by 337div_posNat.cast_pos · cited by 113Nat.cast_posInt.cast_pos · cited by 24Int.cast_posRat.cast_def · cited by 20Rat.cast_defRat.pos · cited by 17Rat.posRat.num_pos · cited by 2Rat.num_posRat.cast_pos_of_posCITED BYCITES

Cites9

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

Cited by1

Results whose statement or proof uses this declaration.