Mathlib Map

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.

Int.castRingHom · cited by 254Int.castRingHomInt.cast_pow · cited by 59Int.cast_powMatrix.det_mul · cited by 51Matrix.det_mulMatrix.det_fromBlocks_zero₂₁ · cited by 10Matrix.det_fromBlocks_zer…Matrix.det_succ_row · cited by 6Matrix.det_succ_rowZsqrtd.norm_eq_mul_conj · cited by 5Zsqrtd.norm_eq_mul_conjfwdDiff_iter_eq_sum_shift · cited by 5fwdDiff_iter_eq_sum_shiftRat.cast_divInt_of_ne_zero · cited by 5Rat.cast_divInt_of_ne_zeroRat.cast_injective · cited by 5Rat.cast_injectiveComplex.tan_add · cited by 5Complex.tan_addGaussianInt.intCast_real_norm · cited by 4GaussianInt.intCast_real_…LieAlgebra.IsKilling.apply_coroot_eq_cast' · cited by 4IsKilling.apply_coroot_eq…RootPairing.chainBotCoeff_sub_chainTopCoeff · cited by 4RootPairing.chainBotCoeff…LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt · cited by 3IsKilling.rootSpace_neg_n…ZMod.mul_inv_eq_gcd · cited by 3ZMod.mul_inv_eq_gcdone_mul · cited by 2841one_mulNat.cast_one · cited by 2501Nat.cast_oneNat.cast_zero · cited by 1870Nat.cast_zeroMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_mulneg_mul · cited by 654neg_mulNat.cast_add · cited by 586Nat.cast_addneg_zero · cited by 542neg_zeroNonAssocRing · cited by 483NonAssocRingInt.cast_natCast · cited by 393Int.cast_natCastInt.cast_one · cited by 371Int.cast_oneadd_mul · cited by 363add_mulneg_add_rev · cited by 236neg_add_revInt.cast_neg · cited by 224Int.cast_negInt.cast_zero · cited by 188Int.cast_zeroInt.cast_add · cited by 124Int.cast_addInt.cast_mulCITED BYCITES

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by114

Results whose statement or proof uses this declaration.