[Merged by Bors] - feat: port of Data.Nat.Gcd.Basic#965
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siddhartha-gadgil wants to merge 3 commits intomasterfrom
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[Merged by Bors] - feat: port of Data.Nat.Gcd.Basic#965siddhartha-gadgil wants to merge 3 commits intomasterfrom
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In future, commit the Mathlib3Port file without editing it so it is easier to compare.
| · rintro ⟨y, z, hy, hz, rfl⟩ | ||
| exact mul_dvd_mul hy hz | ||
| #align nat.dvd_mul Nat.dvd_mul | ||
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Mathlib/Data/Nat/Gcd/Basic.lean
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| #check Nat.dvd_mul_right |
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| #check Nat.dvd_mul_right |
| -- @[simp] | ||
| theorem coprime_one_right_iff (n : ℕ) : coprime n 1 ↔ True := by simp [coprime] | ||
| #align nat.coprime_one_right_iff Nat.coprime_one_right_iff | ||
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| Nat.coprime a (b ^ n) ↔ Nat.coprime a b := by | ||
| rw [Nat.coprime_comm, coprime_pow_left_iff hn, Nat.coprime_comm] | ||
| #align nat.coprime_pow_right_iff Nat.coprime_pow_right_iff | ||
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Mathlib/Data/Nat/Gcd/Basic.lean
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| See also `nat.coprime_of_dvd` and `nat.coprime_of_dvd'` to prove `nat.coprime m n`. | ||
| -/ | ||
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Mathlib/Data/Nat/Gcd/Basic.lean
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| #check Nat.coprime |
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| #check Nat.coprime |
Mathlib/Data/Nat/Gcd/Basic.lean
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| namespace Nat | ||
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| /-! ### `gcd` -/ | ||
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Mathlib/Data/Nat/Gcd/Basic.lean
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| # Definitions and properties of `nat.gcd`, `nat.lcm`, and `nat.coprime` | ||
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| Generalizations of these are provided in a later file as `gcd_monoid.gcd` and | ||
| `gcd_monoid.lcm`. | ||
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| Note that the global `is_coprime` is not a straightforward generalization of `nat.coprime`, see | ||
| `nat.is_coprime_iff_coprime` for the connection between the two. |
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| # Definitions and properties of `nat.gcd`, `nat.lcm`, and `nat.coprime` | |
| Generalizations of these are provided in a later file as `gcd_monoid.gcd` and | |
| `gcd_monoid.lcm`. | |
| Note that the global `is_coprime` is not a straightforward generalization of `nat.coprime`, see | |
| `nat.is_coprime_iff_coprime` for the connection between the two. | |
| # Definitions and properties of `Nat.gcd`, `Nat.lcm`, and `Nat.coprime` | |
| Generalizations of these are provided in a later file as `gcd_monoid.gcd` and | |
| `gcd_monoid.lcm`. | |
| Note that the global `IsCoprime` is not a straightforward generalization of `Nat.coprime`, see | |
| `nat.is_coprime_iff_coprime` for the connection between the two. |
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tracking cf9386b56953fb40904843af98b7a80757bbe7f9 Most of the code was already ported to Std. A couple of lemmas gave a linting error with simp normal form. I have commented out the simp attribute for this. Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>
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Regenerated from the [port status wiki page](https://github.com/leanprover-community/mathlib/wiki/mathlib4-port-status). Relates to the following PRs: * `algebra.euclidean_domain.basic`: leanprover-community/mathlib4#919 * `algebra.field.basic`: leanprover-community/mathlib4#975 * `algebra.group.opposite`: leanprover-community/mathlib4#912 * `algebra.group.prod`: leanprover-community/mathlib4#968 * `algebra.group.with_one.units`: leanprover-community/mathlib4#955 * `algebra.group_power.ring`: leanprover-community/mathlib4#979 * `algebra.hom.equiv.type_tags`: leanprover-community/mathlib4#943 * `algebra.hom.ring`: leanprover-community/mathlib4#958 * `algebra.invertible`: leanprover-community/mathlib4#930 * `algebra.order.field.canonical.basic`: leanprover-community/mathlib4#1018 * `algebra.order.field.canonical.defs`: leanprover-community/mathlib4#985 * `algebra.order.field.inj_surj`: leanprover-community/mathlib4#1017 * `algebra.order.group.densely_ordered`: leanprover-community/mathlib4#956 * `algebra.order.group.min_max`: leanprover-community/mathlib4#933 * `algebra.order.group.prod`: leanprover-community/mathlib4#1026 * `algebra.order.group.with_top`: leanprover-community/mathlib4#946 * `algebra.order.hom.monoid`: leanprover-community/mathlib4#944 * `algebra.order.monoid.prod`: leanprover-community/mathlib4#987 * `algebra.order.monoid.to_mul_bot`: leanprover-community/mathlib4#1024 * `algebra.order.ring.abs`: leanprover-community/mathlib4#929 * `algebra.order.ring.cone`: leanprover-community/mathlib4#935 * `algebra.order.sub.basic`: leanprover-community/mathlib4#936 * `algebra.order.sub.with_top`: leanprover-community/mathlib4#932 * `algebra.order.with_zero`: leanprover-community/mathlib4#903 * `combinatorics.quiver.arborescence`: leanprover-community/mathlib4#997 * `combinatorics.quiver.cast`: leanprover-community/mathlib4#990 * `control.traversable.lemmas`: leanprover-community/mathlib4#948 * `data.bool.set`: leanprover-community/mathlib4#960 * `data.int.cast.field`: leanprover-community/mathlib4#1016 * `data.int.cast.lemmas`: leanprover-community/mathlib4#995 * `data.int.cast.prod`: leanprover-community/mathlib4#1015 * `data.int.div`: leanprover-community/mathlib4#1011 * `data.int.dvd.basic`: leanprover-community/mathlib4#996 * `data.int.order.basic`: leanprover-community/mathlib4#938 * `data.nat.cast.basic`: leanprover-community/mathlib4#980 * `data.nat.cast.prod`: leanprover-community/mathlib4#1010 * `data.nat.cast.with_top`: leanprover-community/mathlib4#1019 * `data.nat.gcd.basic`: leanprover-community/mathlib4#965 * `data.nat.order.basic`: leanprover-community/mathlib4#907 * `data.nat.order.lemmas`: leanprover-community/mathlib4#927 * `data.nat.set`: leanprover-community/mathlib4#961 * `data.nat.upto`: leanprover-community/mathlib4#1020 * `data.pequiv`: leanprover-community/mathlib4#1008 * `data.set.basic`: leanprover-community/mathlib4#892 * `data.set.bool_indicator`: leanprover-community/mathlib4#988 * `data.set.image`: leanprover-community/mathlib4#949 * `data.set.n_ary`: leanprover-community/mathlib4#969 * `data.set.opposite`: leanprover-community/mathlib4#983 * `data.set.prod`: leanprover-community/mathlib4#1004 * `data.set.sigma`: leanprover-community/mathlib4#982 * `data.set_like.basic`: leanprover-community/mathlib4#993 * `data.two_pointing`: leanprover-community/mathlib4#984 * `logic.embedding.set`: leanprover-community/mathlib4#986 * `logic.equiv.embedding`: leanprover-community/mathlib4#1021 * `order.directed`: leanprover-community/mathlib4#963 * `order.rel_iso.set`: leanprover-community/mathlib4#1005 * `order.well_founded`: leanprover-community/mathlib4#970 * `ring_theory.coprime.basic`: leanprover-community/mathlib4#899 Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
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tracking cf9386b56953fb40904843af98b7a80757bbe7f9
Most of the code was already ported to Std. A couple of lemmas gave a linting error with simp normal form. I have commented out the simp attribute for this.