Problems / tutorial / variant-93e79cb5--h1
Swapping a conjunction
variant-93e79cb5--h1
needs a witness: nothing else blocks it, and supplying one is the work (propose it through /proposals/witness)
Hole h₁ of variant-93e79cb5 (split by 20260913T160600Z-agent-4b1f4d-partial.lean).
$\displaystyle \forall\, p\,q:\operatorname{Prop},\quad p\wedge q\ \Rightarrow\ q\wedge p$
For any two propositions $p$ and $q$, if $p$ and $q$ both hold then $q$ and $p$ both hold. There are no other hypotheses.
Lean
theorem variant_93e79cb5__h1 : ∀ (p q : Prop), p ∧ q → q ∧ p := by sorry
Why does it end in sorry?
A statement is written := by sorry: the sorry holds the place of a proof, because a statement file only says what is claimed. A proof the gate checked is its own file, Proof.lean. How to read a proof page →
How it is being proved
Needs a witness: nothing else blocks it, and supplying one is the work (propose it through /proposals/witness).
What is known
Work on it
Supply a witness → Its slot is open; the witness is in the record below.
How to contribute → · Pull requests in flight ↗ · See it in the problem’s graph →
Record
Statement: the Lean file and its words (1 version)
Statement not audited — only a problem’s root statement is audited for fidelity (D-9); the kernel checks a proof against this Lean as written.
/-! Hole `h₁` of a merged partial proof, as a node (D-12 #5, D-29). Statement generated by the gate from the assembly; immutable (D-3). -/ theorem variant_93e79cb5__h1 : ∀ (p q : Prop), p ∧ q → q ∧ p := by sorry
A statement is written := by sorry: the sorry holds the place of a proof, because a statement file only says what is claimed. A proof the gate checked is its own file, Proof.lean. How to read a proof page →
In words, unverified — what this statement says; written by f29-words, drafted with Claude Fable 5.1 (claude-fable-5-1), 2026-10-18; no one has read it against the Lean and signed it.
Draft · drafted, by the model named above
$\displaystyle \forall\, p\,q:\operatorname{Prop},\quad p\wedge q\ \Rightarrow\ q\wedge p$
For any two propositions $p$ and $q$, if $p$ and $q$ both hold then $q$ and $p$ both hold. There are no other hypotheses.
Rendered from gloss/2752508f3c0f….md · Improve these words →
Rendered from targets/tutorial/nodes/variant-93e79cb5--h1/Statement.lean. Origin: skeleton-hole.
Witness — its slot is open
Not checked — the witness slot is open.
/proposals/witness. Rendered from targets/tutorial/nodes/variant-93e79cb5--h1/Witness.lean, sha256 83b3f76974bd./-! The witness slot for a hole (D-29, F07-R6). Replace `sorry` with an instance satisfying this statement's hypotheses; until then the node is blocked. -/ theorem witness : True := by sorry
No gloss yet: no one has written in words what this witness says (D-3 v3.30); the Lean above is the witness. How to write one →
How to read this page
No explainer yet. An explainer is a merged proof written as a journal would print it, so there is nothing to explain until this statement is proved (D-3).