[Merged by Bors] - feat(algebra/algebra/basic algebra/module/basic): add 3 lemmas m • (1 : R) = ↑m #7094
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adomani
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Could you add the same results for ℤ (in a ring) and ℚ (in a division ring/field)? |
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@Vierkantor I had forgotten about your suggestion, but I am also failing to prove the result. Below are the statements that I am trying to prove: let me know if what I am trying to prove is not true! lemma rat.smul_one_eq_coe {R : Type*} [division_ring R] [semimodule ℚ R] (m : ℚ) :
m • (1 : R) = ↑m :=
sorry
lemma int.smul_one_eq_coe {R : Type*} [ring R] [semimodule ℤ R] (m : ℤ) :
m • (1 : R) = ↑m :=
sorry |
Vierkantor
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Apr 8, 2021
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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Ah, |
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For the other, you're right that it doesn't seem provable: we need to assume an lemma rat.smul_one_eq_coe {R : Type*} [division_ring R] [algebra ℚ R] (m : ℚ) :
m • (1 : R) = ↑m :=
by rw [algebra.smul_def, mul_one, ring_hom.eq_rat_cast] |
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Thanks, Anne! I just pushed your suggestions! |
Vierkantor
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bors merge |
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Apr 11, 2021
… : R) = ↑m (#7094) Three lemmas asserting `m • (1 : R) = ↑m`, where `m` is a natural number, an integer or a rational number. Zulip: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/.60smul_one_eq_coe.60 Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
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Apr 12, 2021
…imp` lemmas (#7166) The three lemmas in the merged PR #7094 could be simp lemmas. This PR makes this suggestion. While I was at it, * I moved one of the lemmas outside of the `alg_hom` namespace, * I fixed a typo in a doc string of a tutorial. Zulip: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/trying.20out.20a.20.60simp.60.20lemma
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Three lemmas asserting
m • (1 : R) = ↑m, wheremis a natural number, an integer or a rational number.Zulip:
https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/.60smul_one_eq_coe.60
Co-authored-by: Anne Baanen Vierkantor@users.noreply.github.com