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Proof step 51 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), err = ESUCCESS, icache = icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))], ino0 ≠ 0, afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files0, ¬ str ∈ entries1, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟪icache_set# (getinode (mkdentry(str, ino0).ino, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, icache); dcache_set#(m1, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ dcache-cons (dcache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ pcache-cons (pcache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ synced(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], icache, pcache) ∧ (asynced1 → synced((files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)], icache, pcache)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 52:
asynced ↔ false, dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), err = ESUCCESS, icache = icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))], inode = getinode (mkdentry(str, ino0).ino, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), mkdentry(str, ino0).dentry?, afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); dcache_set#(m1, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ dcache-cons (dcache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ pcache-cons (pcache, dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ synced(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], icache, pcache) ∧ (asynced1 → synced((files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)], icache, pcache))), ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1

Rule argument

pos: right 1

Additional information

Used simplifier rules: icache_set#(INODE, DIRTY; ERR, ICACHE) {ICACHE[INODE.ino] := mkientry(DIRTY, INODE)};% ⊦ mkdentry(str, m).dentry?; (s)