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feat(Data/ENat/Basic): add ENat.toNat_pos #39671

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feat(Data/ENat/Basic): add ENat.toNat_pos #39671

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tb65536 May 21, 2026
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tb65536 May 21, 2026
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4 changes: 4 additions & 0 deletions Mathlib/Data/ENat/Basic.lean
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Expand Up @@ -166,6 +166,10 @@ theorem toNat_top : toNat ⊤ = 0 :=

@[simp] theorem toNat_eq_zero : toNat n = 0 ↔ n = 0 ∨ n = ⊤ := WithTop.untopD_eq_self_iff

theorem toNat_pos (hn0 : n ≠ 0) (hxt : n ≠ ⊤) : 0 < n.toNat := by
rw [pos_iff_ne_zero, ne_eq, ENat.toNat_eq_zero, not_or]
exact ⟨hn0, hxt⟩

theorem lift_eq_toNat_of_lt_top {x : ℕ∞} (hx : x < ⊤) : x.lift hx = x.toNat := by
rcases x with ⟨⟩ | x
· contradiction
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