Further lemmas about the natural numbers #
The distinction between this file and Mathlib.Algebra.Order.Ring.Nat
is not particularly clear.
They are separated for now to minimize the porting requirements for tactics during the transition to
mathlib4. After Mathlib.Algebra.Order.Ring.Rat
has been ported,
please feel free to reorganize these two files.
Sets #
instance
Nat.Subtype.orderBot
(s : Set ℕ)
[DecidablePred fun (x : ℕ) => x ∈ s]
[h : Nonempty ↑s]
:
OrderBot ↑s
Equations
Equations
- Nat.Subtype.semilatticeSup s = let __src := Subtype.instLinearOrder s; let __src_1 := LinearOrder.toLattice; SemilatticeSup.mk ⋯ ⋯ ⋯