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Theorems · Theorem · general algebraic systems

Pi.apply_single

∀ {ι : Type u_1} {M : ι → Type u_6} {N : ι → Type u_7} [inst : (i : ι) → Zero (M i)] [inst_1 : (i : ι) → Zero (N i)]
  [inst_2 : DecidableEq ι] (f' : (i : ι) → M i → N i),
  (∀ (i : ι), f' i 0 = 0) → ∀ (i : ι) (x : M i) (j : ι), f' j (Pi.single i x j) = Pi.single i (f' i x) j
Defined in
Mathlib.Algebra.Notation.Pi.Basic
Cited by
11 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ZeroZeroDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.diagonal_mulVec_single · cited by 3Matrix.diagonal_mulVec_si…Pi.single_op · cited by 3Pi.single_opPi.star_single · cited by 2Pi.star_singlePi.nnnorm_single · cited by 2Pi.nnnorm_singlePi.single_mul_left_apply · cited by 1Pi.single_mul_left_applyPi.single_mul_right_apply · cited by 1Pi.single_mul_right_applyLinearMap.apply_single · cited by 1LinearMap.apply_singleIsAdjoinRootMonic.coeff_algebraMap · cited by 0IsAdjoinRootMonic.coeff_a…LinearIsometryEquiv.piLpCongrRight_single · cited by 0LinearIsometryEquiv.piLpC…Matrix.single_vecMul_diagonal · cited by 0Matrix.single_vecMul_diag…DFinsupp.sumAddHom_piSingle · cited by 0DFinsupp.sumAddHom_piSing…Pi.single · cited by 518Pi.singleFunction.update · cited by 502Function.updateFunction.apply_update · cited by 9Function.apply_updateFunction.update.congr_simp · cited by 7update.congr_simpPi.apply_singleCITED BYCITES

Cites4

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

Cited by11

Results whose statement or proof uses this declaration.