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Proof step 32 from proof links-add-entry (previous step)

p_ino ∈ dirs, m ∈ dirs, ¬ str ∈ entries ∨ entries[str] ≠ ino0 ⊦ str0 ∈ (m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]);dirs[m]).entries ∧ ino0 = (m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]);dirs[m]).entries[str0] ↔ str0 ∈ (m = p_ino ⊃ mkdir(m0, md, n, n0, entries);dirs[m]).entries ∧ ino0 = (m = p_ino ⊃ mkdir(m0, md, n, n0, entries);dirs[m]).entries[str0], ino = ino0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
(m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]);dirs[m]) = mkdir(m1, md0, m2, m3, entries0), m ∈ dirs, p_ino ∈ dirs, ¬ str ∈ entries ∨ entries[str] ≠ ino0 ⊦ str0 ∈ entries0 ∧ ino0 = entries0[str0] ↔ str0 ∈ (m = p_ino ⊃ mkdir(m0, md, n, n0, entries);dirs[m]).entries ∧ ino0 = (m = p_ino ⊃ mkdir(m0, md, n, n0, entries);dirs[m]).entries[str0], ino = ino0

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [(m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]) ;dirs[m] ), m1, md0, m2, m3, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: (m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino]);dirs[m]), m1, md0, m2, m3, entries0