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chore: add simp to aleph0_lt_univ, etc (#37967)
Used in the CGT repo.
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Mathlib/SetTheory/Ordinal/Univ.lean

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@@ -133,14 +133,18 @@ theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} :
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rw [lift_lift, lift_univ, univ_umax.{u, v}] at this
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exact this
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@[simp]
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theorem aleph0_lt_univ : ℵ₀ < univ.{u, v} := by
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simpa using lift_lt_univ' ℵ₀
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@[simp]
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theorem nat_lt_univ (n : ℕ) : n < univ.{u, v} := natCast_lt_aleph0.trans aleph0_lt_univ
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@[simp]
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theorem univ_pos : 0 < univ.{u, v} :=
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aleph0_pos.trans aleph0_lt_univ
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aleph0_lt_univ.pos
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@[simp]
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theorem univ_ne_zero : univ.{u, v} ≠ 0 :=
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univ_pos.ne'
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