UnionFree.lean`

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2 declarations, 0 contain sorry, 0 declared as axioms

Union-free families

A family of sets is union-free if no member is the union of two other distinct members.

Imports (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

def Finset.UnionFree A family F of finsets is union-free if there are no solutions to A ∪ B = C with A, B, C distinct members of F line 34 source
Source documentation
A family F of finsets is union-free if there are no solutions to A ∪ B = C with A, B, C distinct members of F.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: DecidableEq, Finset
Proof uses: Set.Triplewise, Ne, Union.union
3 instances, coercions and auxiliary constants left out.
```
def UnionFree {α : Type*} [DecidableEq α] (F : Finset (Finset α)) : Prop :=
…
```
def Finset.SubfamilyUnionFree A family F of finsets is subfamily union-free if no member is the union of a nonempty subfamily of the others line 40 source
Source documentation
A family F of finsets is subfamily union-free if no member is the union of a nonempty subfamily of the others. This is the arbitrary-subfamily strengthening of UnionFree, which only rules out unions of two members.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: DecidableEq, Finset
Proof uses: Membership.mem, LE.le, Finset.erase, Finset.Nonempty, Ne, Finset.sup, id
9 instances, coercions and auxiliary constants left out.
```
def SubfamilyUnionFree {α : Type*} [DecidableEq α] (F : Finset (Finset α)) : Prop :=
…
```