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Theorems · Theorem · number theory

PosNum.cast_lt

∀ {α : Type u_1} [inst : Semiring α] [inst_1 : PartialOrder α] [IsStrictOrderedRing α] {m n : PosNum}, ↑m < ↑n ↔ m < n
Defined in
Mathlib.Data.Num.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderIsStrictOrderedRing
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Around this declaration

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

PosNum.pred_to_nat · cited by 0PosNum.pred_to_natPosNum.cast_le · cited by 0PosNum.cast_leSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingPosNum · cited by 171PosNumNat.cast_lt · cited by 80Nat.cast_ltcastPosNum · cited by 74castPosNumPosNum.cast_to_nat · cited by 15PosNum.cast_to_natPosNum.lt_to_nat · cited by 2PosNum.lt_to_natPosNum.cast_ltCITED BYCITES

Cites8

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.