[Merged by Bors] - feat: port Algebra.Quaternion #3776
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Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
eric-wieser
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May 3, 2023
Mathlib/Algebra/Quaternion.lean
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| @@ -55,19 +55,19 @@ quaternion | |||
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| /- ./././Mathport/Syntax/Translate/Command.lean:429:34: infer kinds are unsupported in Lean 4: mk {} -/ | |||
| /-- Quaternion algebra over a type with fixed coefficients $a=i^2$ and $b=j^2$. | |||
| Implemented as a structure with four fields: `re`, `im_i`, `im_j`, and `im_k`. -/ | |||
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Note these names in comments will need fixing.
eric-wieser
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May 3, 2023
| @@ -1716,6 +1716,10 @@ theorem toNat_cast (n : ℕ) : Cardinal.toNat n = n := by | |||
| exact (Classical.choose_spec (lt_aleph0.1 (nat_lt_aleph0 n))).symm | |||
| #align cardinal.to_nat_cast Cardinal.toNat_cast | |||
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| @[simp] | |||
| theorem toNat_ofNat (n : ℕ) [n.AtLeastTwo] : Cardinal.toNat (OfNat.ofNat n) = OfNat.ofNat n := | |||
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See https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Cast/Defs.html#instOfNat
We have separate instances for OfNat R 0, OfNat R 1, and [n.AtLeastTwo] : OfNat R n.
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
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The section about
DivisionRinginstance fails, even with η-experiment. I don't know how to fix it.