Skip to content

Commit 5405d5c

Browse files
committed
fix merge
1 parent 0216ec2 commit 5405d5c

File tree

2 files changed

+6
-6
lines changed

2 files changed

+6
-6
lines changed

Mathlib/SetTheory/Cardinal/Basic.lean

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -850,11 +850,11 @@ alias isSuccLimit_zero := isSuccPrelimit_zero
850850

851851
end deprecated
852852

853-
/-- A cardinal is a strong limit if it is not zero and it is closed under powersets. Note that `ℵ₀`
854-
is a strong limit by this definition. -/
853+
/-- A cardinal is a strong limit if it is not zero and it is closed under powersets.
854+
Note that `ℵ₀` is a strong limit by this definition. -/
855855
structure IsStrongLimit (c : Cardinal) : Prop where
856856
ne_zero : c ≠ 0
857-
two_power_lt {x} : x < c → 2 ^ x < c
857+
two_power_lt ⦃x⦄ : x < c → 2 ^ x < c
858858

859859
protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c := by
860860
rw [Cardinal.isSuccLimit_iff]

Mathlib/SetTheory/Cardinal/Cofinality.lean

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -806,7 +806,7 @@ theorem mk_bounded_subset {α : Type*} (h : ∀ x < #α, 2 ^ x < #α) {r : α
806806
constructor
807807
rintro ⟨s, hs⟩
808808
exact (not_unbounded_iff s).2 hs (unbounded_of_isEmpty s)
809-
have h' : IsStrongLimit #α := ⟨ha, @h⟩
809+
have h' : IsStrongLimit #α := ⟨ha, h⟩
810810
have ha := h'.aleph0_le
811811
apply le_antisymm
812812
· have : { s : Set α | Bounded r s } = ⋃ i, 𝒫{ j | r j i } := setOf_exists _
@@ -831,7 +831,7 @@ theorem mk_subset_mk_lt_cof {α : Type*} (h : ∀ x < #α, 2 ^ x < #α) :
831831
#{ s : Set α // #s < cof (#α).ord } = #α := by
832832
rcases eq_or_ne #α 0 with (ha | ha)
833833
· simp [ha]
834-
have h' : IsStrongLimit #α := ⟨ha, @h⟩
834+
have h' : IsStrongLimit #α := ⟨ha, h⟩
835835
rcases ord_eq α with ⟨r, wo, hr⟩
836836
haveI := wo
837837
apply le_antisymm
@@ -1146,7 +1146,7 @@ def IsInaccessible (c : Cardinal) :=
11461146

11471147
theorem IsInaccessible.mk {c} (h₁ : ℵ₀ < c) (h₂ : c ≤ c.ord.cof) (h₃ : ∀ x < c, 2 ^ x < c) :
11481148
IsInaccessible c :=
1149-
⟨h₁, ⟨h₁.le, h₂⟩, (aleph0_pos.trans h₁).ne', @h₃⟩
1149+
⟨h₁, ⟨h₁.le, h₂⟩, (aleph0_pos.trans h₁).ne', h₃⟩
11501150

11511151
-- Lean's foundations prove the existence of ℵ₀ many inaccessible cardinals
11521152
theorem univ_inaccessible : IsInaccessible univ.{u, v} :=

0 commit comments

Comments
 (0)