feat(number_theory/divisors): add divisors_mul #17041
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Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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| rcases m.eq_zero_or_pos with rfl | hm, | ||
| { simp }, | ||
| rcases n.eq_zero_or_pos with rfl | hn, | ||
| { simp }, | ||
| ext i, | ||
| simp only [hm.ne', hn.ne', finset.mem_mul, mem_divisors, ne.def, nat.mul_eq_zero, or_self, | ||
| not_false_iff, and_true, dvd_mul], |
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| rcases m.eq_zero_or_pos with rfl | hm, | |
| { simp }, | |
| rcases n.eq_zero_or_pos with rfl | hn, | |
| { simp }, | |
| ext i, | |
| simp only [hm.ne', hn.ne', finset.mem_mul, mem_divisors, ne.def, nat.mul_eq_zero, or_self, | |
| not_false_iff, and_true, dvd_mul], | |
| simp_rw [ext_iff, mem_mul, mem_divisors, dvd_mul, ←exists_and_distrib_right, mul_ne_zero_iff], | |
| exact λ x, exists_congr (λ m, exists_congr (λ n, by tauto)), |
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Also fixes some bad indentation in nearby lemmas
Co-authored-by: Bhavik Mehta bhavikmehta8@gmail.com
nat.dvd_mulanddvd_mul#17131