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Proof step 1 from proof links1 (conclusion)

⊦ links(fid, fnode(fid0)) = (fid = fid0 ⊃ {ε} ;∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ps = ps0 ↔ (∀ p. p ∈ ps ↔ p ∈ ps0)
Proof step 3:
⊦ ∀ p. p ∈ links(fid, fnode(fid0)) ↔ p ∈ (fid = fid0 ⊃ {ε} ;∅)

Rule argument

spec: set-basic, inst: pathset name: Extension seq: ⊦ ps = ps0 ↔ (∀ p. p ∈ ps ↔ p ∈ ps0) subst: [ps0, ps] → [(fid = fid0 ⊃ {ε} ;∅), links(fid, fnode(fid0))] flags: <all paths>

Additional information

Used terms: (fid = fid0 ⊃ {ε} ;∅), links(fid, fnode(fid0))