[Merged by Bors] - feat(algebra/ring): the codomain of a ring hom is trivial iff ... #3676
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src/algebra/ring/basic.lean
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| λ h x, set.mem_singleton_iff.mp (h ▸ set.mem_range_self x)⟩ | ||
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| /-- `f : R →+* S` doesn't map `1` to `0` if `S` is nontrivial -/ | ||
| lemma map_one_ne_zero_of_nontrivial [nontrivial β] : f 1 ≠ 0 := |
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I don't think that we should mention of_nontrivial in lemma names. E.g., we avoid it in zero_ne_one. Why should we mention it in ring_hom.map_one_ne_zero? Same for map_monic_ne_zero.
Otherwise LGTM.
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I'll fix @urkud 's suggestion. bors r- |
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Canceled. |
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Forgot to say: clearly, |
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Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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) In the discussion of #3488, Johan (currently on vacation, so I'm not pinging him) noted that we were missing the lemma "if `f` is a ring homomorphism, `∀ x, f x = 0` implies that the codomain is trivial". This PR adds a couple of ways to derive from homomorphisms that rings are trivial. I used `0 = 1` to express that the ring is trivial because that seems to be the one that is used in practice. Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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In the discussion of #3488, Johan (currently on vacation, so I'm not pinging him) noted that we were missing the lemma "if
fis a ring homomorphism,∀ x, f x = 0implies that the codomain is trivial". This PR adds a couple of ways to derive from homomorphisms that rings are trivial.I used
0 = 1to express that the ring is trivial because that seems to be the one that is used in practice.