feat(order/bounded_lattice): with_top.cases #3135
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Adding the case of integers.
jcommelin
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jcommelin
reviewed
Jun 22, 2020
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Johan Commelin <johan@commelin.net>
urkud
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Jun 22, 2020
| @@ -730,6 +730,35 @@ lemma lt_iff_exists_coe_btwn [partial_order α] [densely_ordered α] [no_top_ord | |||
| ⟨λ h, let ⟨y, hy⟩ := dense h, ⟨x, hx⟩ := (lt_iff_exists_coe _ _).1 hy.2 in ⟨x, hx.1 ▸ hy⟩, | |||
| λ ⟨x, hx⟩, lt_trans hx.1 hx.2⟩ | |||
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| /-- Lemma shows that a in with_top Z is either the maximal element or some integer n. -/ | |||
| lemma with_top.cases (a : with_top ℤ) : a = ⊤ ∨ ∃ n : ℤ, a = n := | |||
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This is true for any with_top α. And I would prefer to have with_top.cases_on with the same signature as option.cases_on but using coercion and top instead of some and none (with proof := option.cases_on a).
| end | ||
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| /-- Shows that for a in with_top, a+a = 0 is equivalent to a=0. -/ | ||
| lemma (a : with_top ℤ) : a + a = 0 ↔ a = 0 := |
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We should have instance with_top.char_zero, instance with_top.mul_zero_class, and instance with_top.no_zero_divisors instead. Then one can use add_self_eq_zero directly. Two out of three are now in #3157
bryangingechen
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I've PRed an instance that implies this lemma, closing the PR. Thank you for pointing at a hole in the library! |
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Oct 8, 2020
Motivated by #3135. * Use `R` as a `Type*` variable; * Add `add_monoid_hom.map_nat_cast` and `with_top.coe_add_hom`; * Drop versions of `char_zero_of_inj_zero`, use `[add_left_cancel_monoid R]` instead.
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Sorry about that, I completely forgot about it. Thank you for completing it! |
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Adding the case of integers.