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Proof step 10 from proof links-add-entry (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
(m = p_ino ⊃ mkdir(m0, md, n, n0, entries[str, ino0]);dirs[m]) = mkdir(m1, md0, m2, m3, entries0), p_ino ∈ dirs ⊦ m ∈ dirs ∧ str0 ∈ entries0 ∧ ino0 = entries0[str0] ↔ mklink(m, str0) = mklink(p_ino, str) ∨ m ∈ dirs ∧ 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]

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, ino0]) ;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, ino0]);dirs[m]), m1, md0, m2, m3, entries0