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Proof step 3 from proof subdirs-inc-size (previous step)

p_ino ∈ dirs ⊦ subdirs(ino, dirs[p_ino, mkdir(m0 + 1, md, n0, n1, entries)]) = subdirs(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0)
Proof step 5:
p_ino ∈ dirs ⊦ ∀ str. str ∈ subdirs(ino, dirs[p_ino, mkdir(m0 + 1, md, n0, n1, entries)]) ↔ str ∈ subdirs(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)])

Rule argument

spec: set-basic, inst: dir-entries name: Extension seq: ⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0) subst: [strings0, strings] → [subdirs(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)]), subdirs (ino, dirs[p_ino, mkdir(m0 + 1, md, n0, n1, entries)])] flags: <all paths>

Additional information

Used terms: subdirs(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)]), subdirs(ino, dirs[p_ino, mkdir(m0 + 1, md, n0, n1, entries)])