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Proof step 42 from proof fsync-inode-others-unchanged (previous step)

icache0[m] = mkientry(true, mkinode(m0, md, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size)), err = ESUCCESS, icache1 = icache0, icache-cons(icache0, dirs, files0), m0 ∈ dirs, m ∈ icache0 ⊦ [icache_set_status#(m, false; err, icache1)] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache1)[ino] = (files0 ⊕ icache0)[ino]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
icache0[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), err = ESUCCESS, icache1 = icache0, icache-cons(icache0, dirs, files0), m ∈ icache0, m0 ∈ dirs ⊦ [icache_set_status#(m, false; err, icache1)] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache1)[ino] = (files0 ⊕ icache0)[ino]))

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] → [dirs[m0], m1, md0, m2, m3, entries]

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: dirs[m0], m1, md0, m2, m3, entries