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[Merged by Bors] - feat(Data/Nat/Order/Basic): le_one_iff_eq_zero_or_eq_one #6949

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[Merged by Bors] - feat(Data/Nat/Order/Basic): le_one_iff_eq_zero_or_eq_one #6949

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@mo271 mo271 commented Sep 4, 2023

Open in Gitpod

@mo271 mo271 added awaiting-review The author would like community review of the PR awaiting-CI new-feature Add features not present in Mathlib 3 labels Sep 4, 2023
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mo271 commented Sep 4, 2023

This is basically the not_iff_not of the statement one_lt_iff_ne_zero_and_ne_one just above, but this proof:

theorem le_one_iff_eq_zero_or_eq_one : ∀ {n : ℕ}, n ≤ 1 ↔ n = 0 ∨ n = 1 := by
  refine' not_iff_not.mp _
  rw [Nat.not_le, one_lt_iff_ne_zero_and_ne_one]
  exact not_or.symm

is not nicer...

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Thanks 🎉

bors merge

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-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 Sep 4, 2023
bors bot pushed a commit that referenced this pull request Sep 4, 2023
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feat(Data/Nat/Order/Basic): le_one_iff_eq_zero_or_eq_one (#6949)
a085bc3 
Co-authored-by: Moritz Firsching <firsching@google.com>
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Pull request successfully merged into master.

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@bors bors bot changed the title feat(Data/Nat/Order/Basic): le_one_iff_eq_zero_or_eq_one [Merged by Bors] - feat(Data/Nat/Order/Basic): le_one_iff_eq_zero_or_eq_one Sep 4, 2023
@bors bors bot closed this Sep 4, 2023
@bors bors bot deleted the mo271/le_one_iff_eq_zero_or_eq_one branch September 4, 2023 14:40
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