855.lean`

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 855

Reference: erdosproblems.com/855

This is an "eventually" formulation of the Second Hardy–Littlewood conjecture.

Imports (2)

theorem Erdos855.erdos_855 Erdős Problem 855 (Segal's conjecture): $\pi(x + y) \le \pi(x) + \pi(y)$ for all sufficiently large $x, y$, i.e. for all $x, y \ge N$ for some $N$ sorry line 41 source
Source documentation
Erdős Problem 855 (Segal's conjecture): $\pi(x + y) \le \pi(x) + \pi(y)$ for all sufficiently large $x, y$, i.e. for all $x, y \ge N$ for some $N$.

depends on sorry what this means
Statement uses: Iff, True, Filter.Eventually, Prod, Nat, LE.le, Nat.primeCounting, HAdd.hAdd, Prod.fst, Prod.snd, SProd.sprod, Filter, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_855 : answer(sorry) ↔
    ∀ᶠ (xy : ℕ × ℕ) in atTop ×ˢ atTop, π (xy.1 + xy.2) ≤ π xy.1 + π xy.2 := by
…
```