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Proof step 3 from proof path-split-one (previous step)

dirs[m] = mkdir(n0, md, n, n1, entries), ispath(p, n, m, dirs, files) ⊦ ispath(p + str ', n, entries[str], dirs, files) ↔ m ∈ dirs ∧ str ∈ entries ∧ (entries[str] ∈ files ∨ entries[str] ∈ dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))
Proof step 5:
dirs[m] = mkdir(n0, md, n, n1, entries), ispath(p, n, m, dirs, files) ⊦ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(str ', m0, entries[str], dirs, files)) ↔ m ∈ dirs ∧ str ∈ entries ∧ (entries[str] ∈ files ∨ entries[str] ∈ dirs)

Rule argument

spec: <toplevel> name: path-split seq: ⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files)) subst: [files, dirs, m, n, q, p] → [files, dirs, entries[str], n, str ', p] flags: <all paths>

Additional information

Used terms: files, dirs, entries[str], n, str ', p