Theorems · Theorem · number theory
Int.cast_mul
∀ {α : Type u_1} [inst : NonAssocRing α] (m n : ℤ), ↑(m * n) = ↑m * ↑n- Defined in
- Mathlib.Algebra.Ring.Int.Defs
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 37 from the axioms, rests on 532 definitions · uses propext, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- MulZeroClass.zero_mulproof · cited by 1,625
- neg_mulproof · cited by 654
- Nat.cast_addproof · cited by 586
- neg_zeroproof · cited by 542
- NonAssocRingstatement and proof · cited by 483
- Int.cast_natCastproof · cited by 393
- Int.cast_oneproof · cited by 371
- add_mulproof · cited by 363
- neg_add_revproof · cited by 236
Cited by114
Results whose statement or proof uses this declaration.
- Int.castRingHomproof · cited by 254
- Int.cast_powproof · cited by 59
- Matrix.det_mulproof · cited by 51
- Matrix.det_fromBlocks_zero₂₁proof · cited by 10
- Matrix.det_succ_rowproof · cited by 6
- Zsqrtd.norm_eq_mul_conjproof · cited by 5
- fwdDiff_iter_eq_sum_shiftproof · cited by 5
- Rat.cast_divInt_of_ne_zeroproof · cited by 5
- Rat.cast_injectiveproof · cited by 5
- Complex.tan_addproof · cited by 5
- GaussianInt.intCast_real_normproof · cited by 4
- LieAlgebra.IsKilling.apply_coroot_eq_cast'proof · cited by 4