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chore: bump to v4.22.0 (#306)
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MIL/C09_Groups_and_Rings/S02_Rings.lean

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-- BOTH:
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import Mathlib.RingTheory.Ideal.Quotient.Operations
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import Mathlib.RingTheory.Localization.Basic
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import Mathlib.RingTheory.DedekindDomain.Ideal
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import Mathlib.Analysis.Complex.Polynomial.Basic
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import Mathlib.Data.ZMod.QuotientRing
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import MIL.Common

MIL/C10_Linear_Algebra/S02_Subspaces.lean

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@@ -204,7 +204,7 @@ example {ι : Type*} [DecidableEq ι] (U : ι → Submodule K V) (h : DirectSum.
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(h.submodule_iSupIndep.pairwiseDisjoint hij).eq_bot
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-- Those conditions characterize direct sums.
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#check DirectSum.isInternal_submodule_iff_independent_and_iSup_eq_top
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#check DirectSum.isInternal_submodule_iff_iSupIndep_and_iSup_eq_top
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-- The relation with external direct sums: if a family of subspaces is
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-- in internal direct sum then the map from their external direct sum into `V`

MIL/C10_Linear_Algebra/S04_Bases.lean

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section
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open Module
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variable {ι : Type*} (B : Basis ι K V) (v : V) (i : ι)
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-- The basis vector with index ``i``
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EXAMPLES: -/
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-- QUOTE:
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section
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#check (Module.finrank K V : ℕ)
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-- `Fin n → K` is the archetypical space with dimension `n` over `K`.
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By definition, ``FiniteDimensional K V`` can be read from any basis.
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EXAMPLES: -/
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-- QUOTE:
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variable {ι : Type*} (B : Basis ι K V)
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variable {ι : Type*} (B : Module.Basis ι K V)
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example [Finite ι] : FiniteDimensional K V := FiniteDimensional.of_fintype_basis B
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universe u v -- `u` and `v` will denote universe levels
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variable {ι : Type u} (B : Basis ι K V)
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{ι' : Type v} (B' : Basis ι' K V)
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variable {ι : Type u} (B : Module.Basis ι K V)
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{ι' : Type v} (B' : Module.Basis ι' K V)
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example : Cardinal.lift.{v, u} (.mk ι) = Cardinal.lift.{u, v} (.mk ι') :=
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mk_eq_mk_of_basis B B'

lake-manifest.json

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lakefile.toml

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[[require]]
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name = "mathlib"
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git = "https://github.com/leanprover-community/mathlib4"
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rev = "v4.21.0"
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rev = "v4.22.0"
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[[lean_lib]]
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name = "MIL"

lean-toolchain

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leanprover/lean4:v4.21.0
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leanprover/lean4:v4.22.0

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