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Proof step 44 from proof fsync-inode-overwrite (previous step)

icache[m] = mkientry(true, mkinode(m2, md, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size)), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, m2 ∈ dirs ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → files0[m2] = (files0 ⊕ icache0)[m2])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m2, md, true, m4, m5, m3)), dirs[m2] = mkdir(m3, md1, m4, m5, entries), err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m2 ∈ dirs, m ∈ icache, m ∈ files0 ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → files0[m2] = (files0 ⊕ icache0)[m2])

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[m2], m3, md1, m4, m5, 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[m2], m3, md1, m4, m5, entries