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Proof step 13 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, ino0]);dirs[m]) = mkdir(m1, md0, m2, m3, entries0), m = p_ino, p_ino ∈ dirs ⊦ m ∈ dirs ∧ str0 ∈ entries0 ∧ ino0 = entries0[str0] ↔ mklink(m, str0) = mklink(p_ino, str) ∨ m ∈ dirs ∧ str0 ∈ entries1 ∧ ino0 = entries1[str0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
p_ino ∈ dirs ⊦ str0 ∈ entries1[str, ino0] ∧ ino0 = entries1[str, ino0][str0] ↔ mklink(p_ino, str0) = mklink(p_ino, str) ∨ str0 ∈ entries1 ∧ ino0 = entries1[str0]

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)