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Proof step 9 from proof links-putnew (previous step)

(m0 = ino ⊃ mkdir(m, md, n, n0, ∅);(dirs ++ ino)[m0]) = mkdir(m1, md0, m2, m3, entries) ⊦ (m0 = ino ∨ m0 ∈ dirs) ∧ str ∈ entries ∧ ino0 = entries[str] ↔ m0 ∈ dirs ∧ str ∈ dirs[m0].entries ∧ ino0 = dirs[m0].entries[str], ino = 0, ino ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
(m0 = ino ⊃ mkdir(m, md, n, n0, ∅);dirs[m0]) = mkdir(m1, md0, m2, m3, entries) ⊦ (m0 = ino ∨ m0 ∈ dirs) ∧ str ∈ entries ∧ ino0 = entries[str] ↔ m0 ∈ dirs ∧ str ∈ dirs[m0].entries ∧ ino0 = dirs[m0].entries[str], ino = 0, ino ∈ dirs

Rule argument

Additional information

Used simplifier rules: ino ∈ dirs, ino0 ≠ 0, ¬ ino0 ∈ dirs ⊦ ino ≠ ino0 → (dirs ++ ino0)[ino] = dirs[ino]; (s)