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[Merged by Bors] - feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff #11132

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[Merged by Bors] - feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff #11132

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@jsm28 jsm28 commented Mar 3, 2024

Add the two lemmas

lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by

and

lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by

Feel free to golf.

From AperiodicMonotilesLean.

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@jsm28
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff
7f472b5 
Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
@jsm28 jsm28 added awaiting-review The author would like community review of the PR easy < 20s of review time. See the lifecycle page for guidelines. labels Mar 3, 2024
alreadydone
alreadydone approved these changes Mar 3, 2024
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LGTM
maintainer merge

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github-actions bot commented Mar 3, 2024

🚀 Pull request has been placed on the maintainer queue by alreadydone.

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Thanks!

bors merge

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review The author would like community review of the PR labels Mar 3, 2024
mathlib-bors bot pushed a commit that referenced this pull request Mar 3, 2024
@jsm28
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff (#11132
8102736 
)

Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
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mathlib-bors bot commented Mar 3, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff [Merged by Bors] - feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff Mar 3, 2024
@mathlib-bors mathlib-bors bot closed this Mar 3, 2024
@mathlib-bors mathlib-bors bot deleted the jsm28/cardinal_inf_eq_zero_iff branch March 3, 2024 21:54
kbuzzard pushed a commit that referenced this pull request Mar 12, 2024
@jsm28 @kbuzzard
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff (#11132
208cf31 
)

Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
dagurtomas pushed a commit that referenced this pull request Mar 22, 2024
@jsm28 @dagurtomas
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff (#11132
10b31de 
)

Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
utensil pushed a commit that referenced this pull request Mar 26, 2024
@jsm28 @utensil
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff (#11132
13b4a29 
)

Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
Louddy pushed a commit that referenced this pull request Apr 15, 2024
@jsm28 @Louddy
feat(SetTheory/Cardinal): sInf_eq_zero_iff, iInf_eq_zero_iff (#11132
6e7a0c3 
)

Add the two lemmas

```lean
lemma sInf_eq_zero_iff {s : Set Cardinal} : sInf s = 0 ↔ s = ∅ ∨ ∃ a ∈ s, a = 0 := by
```

and

```lean
lemma iInf_eq_zero_iff {ι : Sort*} {f : ι → Cardinal} :
    (⨅ i, f i) = 0 ↔ IsEmpty ι ∨ ∃ i, f i = 0 := by
```

Feel free to golf.

From AperiodicMonotilesLean.
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