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Proof step 38 from proof fsync-inode-keep-abs (previous step)

icache[m] = mkientry(true, mkinode(m0, md, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size)), err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ dirs ⊦ [icache_set_status#(m, false; err, icache)] (files0 = (files ⊕ pcache) ⊕ icache)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, icache-cons(icache, dirs, files), m0 ∈ dirs, m ∈ icache ⊦ [icache_set_status#(m, false; err, icache)] (files0 = (files ⊕ pcache) ⊕ icache)

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