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Proof step 8 from proof lastlink-move (previous step)

dirs[ino0] = mkdir(m0, md0, n0, n2, entries0), dirs[ino1] = mkdir(m1, md1, n1, n3, entries1), ino0 ∈ dirs, ino1 ∈ dirs, str0 ∈ entries0, str1 ∈ entries1, ∀ alink0. alink0 ∈ links(entries0[str0], dirs) ↔ alink0 ∈ ∅ ++ alink ⊦ entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
dirs[ino1] = mkdir(m1, md1, n1, n3, entries1), dirs[ino0] = mkdir(m0, md0, n0, n2, entries0), str1 ∈ entries1, str0 ∈ entries0, ino1 ∈ dirs, ino0 ∈ dirs, ∀ alink0. alink0.pino ∈ dirs ∧ alink0.name ∈ dirs[alink0.pino].entries ∧ entries0[str0] = dirs[alink0.pino].entries[alink0.name] ↔ alink0 = alink ⊦ entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1

Rule argument

Additional information

Used simplifier rules: ⊦ alink ∈ ∅ ++ alink0 ↔ alink = alink0; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)