BealConjecture.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

3 declarations, 1 contain sorry, 0 declared as axioms

Beal conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100SolvedSet1.lean

def BealConjecture.bealConjecture line 30 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Proof uses: Nat, Ne, OfNat.ofNat, LT.lt, Eq, HAdd.hAdd, HPow.hPow, Finset.gcd, Insert.insert, Finset, Singleton.singleton, id
14 instances, coercions and auxiliary constants left out.
theorem BealConjecture.beal_conjecture The Beal Conjecture: if we are given positive integers $A, B, C, x, y, z$ such that $x, y, z > 2$ and $A^x + B^y = C^z$ then $A, B, C$ have a common divisor sorry line 39 source
Source documentation
The Beal Conjecture: if we are given positive integers $A, B, C, x, y, z$ such that $x, y, z > 2$ and $A^x + B^y = C^z$ then $A, B, C$ have a common divisor.

depends on sorry what this means
Statement uses: BealConjecture.bealConjecture
Proof uses: Nat, sorryAx, Lean.Name, Ne, OfNat.ofNat, LT.lt, Eq, HAdd.hAdd, HPow.hPow, Finset.gcd, Insert.insert, Finset, Singleton.singleton, id, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
14 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem beal_conjecture : bealConjecture := by
…
```
Mentions: BealConjecture.bealConjecture
theorem BealConjecture.flt_of_beal_conjecture The Beal Conjecture implies Fermat's last theorem line 46 source
Source documentation
The Beal Conjecture implies Fermat's last theorem

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: BealConjecture.bealConjecture, FermatLastTheorem
Proof uses: Nat, GE.ge, OfNat.ofNat, Ne, id, HAdd.hAdd, HPow.hPow, Eq, mul_ne_zero, HMul.hMul, Decidable.byContradiction, Not, And, False, of_eq_true, Eq.trans, True, congr, congrArg, eq_false and 40 more
60 instances, coercions and auxiliary constants left out.

Tactic trace: 28 steps
Open to load the checked before-and-after goal states.
```
theorem flt_of_beal_conjecture (H : bealConjecture) :
    FermatLastTheorem := by
…
```
Mentions: BealConjecture.bealConjecture