[Merged by Bors] - feat(data/zsqrtd/basic): add some lemmas about conj, norm #6715
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Ruben-VandeVelde
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Mar 16, 2021
Ruben-VandeVelde
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eric-wieser
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Mar 17, 2021
src/data/zsqrtd/basic.lean
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| @[simp] lemma conj_zero : conj (0 : ℤ√d) = 0 := | ||
| by rw [ext, conj_re, conj_im, zero_im, zero_re, neg_zero, and_self] |
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Can you use this to show that conj is an add_monoid_hom?
That is, declare
/-- `conj` as an `add_monoid_hom`. -/
def conj_hom : ℤ√d →+ ℤ√d :=
{ to_fun := conj,
map_add' := λ ⟨a, ai⟩ ⟨b, bi⟩, ext.mpr ⟨rfl, neg_add _ _⟩,
map_zero' := ext.mpr ⟨rfl, neg_zero⟩ }And then prove conj_zero, conj_neg, conj_add, conj_sub as conj_hom.map_zero etc.
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Done. (I had to move the conj section below the add_monoid instance.)
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Thanks! Feel free to merge once CI passes bors d+ |
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bors r+ |
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Pull request successfully merged into master. Build succeeded: |
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