AffineSpaceDim.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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Project sources: Pinned project documentation, Polynomial Freiman-Ruzsa proof paper, arXiv v2

5 declarations, 0 contain sorry, 0 declared as axioms

Imports (4)

Imported by 2 files

def AffineSpace.finrank The dimension of the affine span over ℤ of a subset of an additive group line 19 source
Source documentation
The dimension of the affine span over ℤ of a subset of an additive group.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Ring, AddCommGroup, Module, AddTorsor, Set, Nat
Proof uses: Submodule.finrank, vectorSpan
6 instances, coercions and auxiliary constants left out.
```
noncomputable def finrank (s : Set P) : ℕ := (vectorSpan k s).finrank
…
```
lemma AffineSpace.finrank_vadd_set line 23 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Ring, AddCommGroup, Module, AddTorsor, Set, Eq, Nat, AffineSpace.finrank, HVAdd.hVAdd
Proof uses: of_eq_true, Submodule.finrank, vectorSpan, Eq.trans, True, congrFun', congrArg, Submodule, vectorSpan_vadd, eq_self
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma AffineSpace.finrank_empty line 27 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Ring, AddCommGroup, Module, AddTorsor, Nontrivial, Eq, Nat, AffineSpace.finrank, EmptyCollection.emptyCollection, Set, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Submodule.finrank, vectorSpan, Bot.bot, Submodule, vectorSpan_empty, finrank_bot, eq_self
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma AffineSpace.finrank_le_submoduleFinrank line 31 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Ring, AddCommGroup, Module, AddTorsor, Set, Submodule, StrongRankCondition, Module.Finite, Subtype, Membership.mem, VSub.vsub, LE.le, Nat, AffineSpace.finrank, Submodule.finrank
Proof uses: Submodule.finrank_mono, vectorSpan, Eq.mpr, id, Eq, Eq.trans, Submodule.span, forall_congr, implies_congr, Eq.refl, Eq.mp, HSub.hSub, congrArg, vsub_sub_vsub_cancel_right, Submodule.sub_mem
31 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
lemma AffineSpace.finrank_le_moduleFinrank line 37 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Ring, AddCommGroup, Module, AddTorsor, Set, StrongRankCondition, Module.Finite, LE.le, Nat, AffineSpace.finrank, Module.finrank
Proof uses: Submodule.finrank_le, vectorSpan
7 instances, coercions and auxiliary constants left out.