1_35c.lean`

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3 declarations, 1 contain sorry, 0 declared as axioms

Conjecture 1.35(c)

by A. I. Mal'cev and L. Fuchs

Reference: The Kourovka Notebook

Imports (1)

FormalConjecturesUtil

def Kourovka.«1.35c».IsBiInvariant A relation on a group is bi-invariant if it is preserved by both left and right multiplication line 34 source
Source documentation
A relation on a group is bi-invariant if it is preserved by both left and right multiplication.

no axioms what this means
Statement uses: Group
Proof uses: And, HMul.hMul
6 instances, coercions and auxiliary constants left out.
```
def IsBiInvariant (G : Type*) [Group G] (r : G → G → Prop) : Prop :=
…
```
def Kourovka.«1.35c».ProOrderable ProOrderable G means every bi-invariant partial order extends to a bi-invariant linear order line 42 source
Source documentation
ProOrderable G means every bi-invariant partial order extends to a bi-invariant linear order.

no axioms what this means
Statement uses: Group
Proof uses: IsPartialOrder, Kourovka.«1.35c».IsBiInvariant, Exists, And, IsLinearOrder
```
def ProOrderable (G : Type*) [Group G] : Prop :=
…
```
theorem Kourovka.«1.35c».kourovka_1_35c Do there exist simple pro-orderable groups? sorry line 53 source
Source documentation
Do there exist simple pro-orderable groups?

depends on sorry what this means
Statement uses: Iff, True, Exists, Group, And, IsSimpleGroup, Kourovka.«1.35c».ProOrderable
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem kourovka_1_35c : answer(sorry) ↔
    ∃ (G : Type) (_ : Group G), IsSimpleGroup G ∧ ProOrderable G := by
…
```
Mentions: Kourovka.«1.35c».ProOrderable