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[Merged by Bors] - refactor(algebra/{dual_number,triv_sq_zero_ext}): support non-commutative rings #18384

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[Merged by Bors] - refactor(algebra/{dual_number,triv_sq_zero_ext}): support non-commutative rings #18384

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c943860
refactor(algebra/dual_number): support non-commutative rings
eric-wieser Feb 4, 2023
3c4e1a2
nolint
eric-wieser Feb 4, 2023
381d469
Merge remote-tracking branch 'origin/master' into eric-wieser/tsze-no…
eric-wieser Feb 14, 2023
8382c2c
propagate fixes through the topology files
eric-wieser Feb 14, 2023
19f8533
add a more general lemma
eric-wieser Feb 14, 2023
7272211
Apply suggestions from code review
eric-wieser Feb 22, 2023
2a43c9e
fix
eric-wieser Feb 22, 2023
758e697
fix docs
eric-wieser Feb 22, 2023
57242c2
fix typo
eric-wieser Feb 22, 2023
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2 changes: 1 addition & 1 deletion src/algebra/dual_number.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -56,7 +56,7 @@ open triv_sq_zero_ext
@[simp] lemma snd_eps [has_zero R] [has_one R] : snd ε = (1 : R) := snd_inr _ _

/-- A version of `triv_sq_zero_ext.snd_mul` with `*` instead of `•`. -/
@[simp] lemma snd_mul [semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + fst y * snd x :=
@[simp] lemma snd_mul [semiring R] (x y : R[ε]) : snd (x * y) = fst x * snd y + snd x * fst y :=
snd_mul _ _

@[simp] lemma eps_mul_eps [semiring R] : (ε * ε : R[ε]) = 0 := inr_mul_inr _ _ _
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