Theorems · Theorem · number theory
PNat.sub_coe
∀ (a b : ℕ+), ↑(a - b) = if b < a then ↑a - ↑b else 1
- Defined in
- Mathlib.Data.PNat.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_of_not_gtproof · cited by 430
- PNatstatement and proof · cited by 392
- PNat.valstatement and proof · cited by 226
- tsub_eq_zero_iff_leproof · cited by 32
- tsub_pos_of_ltproof · cited by 31
- Nat.toPNat'proof · cited by 6
- PNat.toPNat'_coeproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- PNat.add_sub_of_ltproof · cited by 1
- PNat.sub_leproof · cited by 0
- PNat.le_sub_one_of_ltproof · cited by 0