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Proof step 3 from proof expath-rec (previous step)

dirs[n] = mkdir(m, md, m0, m1, entries) ⊦ ispath(str ' + q, n, dirs, files) ↔ n ∈ dirs ∧ str ∈ entries ∧ ispath(q, entries[str], dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ispath(p, n, dirs, files) ↔ (∃ m. ispath(p, n, m, dirs, files))
Proof step 5:
dirs[n] = mkdir(m, md, m0, m1, entries) ⊦ (∃ m. ispath(str ' + q, n, m, dirs, files)) ↔ n ∈ dirs ∧ str ∈ entries ∧ ispath(q, entries[str], dirs, files)

Rule argument

spec: <toplevel> name: expath seq: ⊦ ispath(p, n, dirs, files) ↔ (∃ m. ispath(p, n, m, dirs, files)) subst: [files, dirs, n, p] → [files, dirs, n, str ' + q] flags: <all paths>

Additional information

Used terms: files, dirs, n, str ' + q