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Proof step 70 from proof fsync-dirs (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m3, md, true, dirs0[m3].nlink, dirs0[m3].nsubdirs, dirs0[m3].size)), err = ESUCCESS, m ∈ icache, m ∈ files0, m3 ∈ dirs0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0[m3, dirs0[m3].meta:= md]; if err = ESUCCESS then afs_fsync#(mkinode(m3, md, true, dirs0[m3].nlink, dirs0[m3].nsubdirs, dirs0[m3].size), false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 71:
icache[m] = mkientry(true, mkinode(m3, md, true, m5, m6, m4)), files0[m] = mkfile(m0, md0, m1, content), dirs0[m3] = mkdir(m4, md1, m5, m6, entries), err = ESUCCESS, m3 ∈ dirs0, m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0[m3, dirs0[m3].meta:= md]; if err = ESUCCESS then afs_fsync#(mkinode(m3, md, true, m5, m6, m4), false, dirs, files; ; asynced2, err)] (dirs = dirs0)

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] → [dirs0[m3], m4, md1, m5, m6, 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: dirs0[m3], m4, md1, m5, m6, entries