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Proof step 35 from proof links-add-entry (previous step)

(m = p_ino ⊃ mkdir(m0, md, n, n0, entries);dirs[m]) = mkdir(m4, md1, m5, m6, entries1), (m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]);dirs[m]) = mkdir(m1, md0, m2, m3, entries0), m = p_ino, m ∈ dirs, p_ino ∈ dirs, ¬ str ∈ entries ∨ entries[str] ≠ ino0 ⊦ str0 ∈ entries0 ∧ ino0 = entries0[str0] ↔ str0 ∈ entries1 ∧ ino0 = entries1[str0], ino = ino0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
p_ino ∈ dirs, str ∈ entries1 ⊦ str0 ∈ entries1[str, ino] ∧ ino0 = entries1[str, ino][str0] ↔ str0 ∈ entries1 ∧ ino0 = entries1[str0], entries1[str] = ino0, ino = ino0

Rule argument

Additional information

Used simplifier rules: ⊦ entries[str, ino][str] = ino; (s)% ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries; (ws)%⊦ str ∈ entries ∧ ¬ str0 ∈ entries → entries[str0, ino][str] = entries[str]; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)