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Proof step 46 from proof inv-create (previous step)

dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries1), err = ESUCCESS, ino0 ≠ 0, afs-cons(dirs0, files0), afs-cons(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files0, ¬ str ∈ entries1, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1), false; err, icache); icache_set# (getinode (mkdentry(str, ino0).ino, dirs0[m, (m ∈ dirs0 ⊃ mkdir(m0 + 1, md2, # links(m, dirs0), m2, entries1[str, ino0]);dirs0[m]).meta:= md0], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, icache); dcache_set# ((m ∈ dirs0 ⊃ mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).meta, false, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).nlink, 0, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).size) ) .ino, str, mkdentry(str, ino0) ; err, dcache)⟫ ( icache-cons(icache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ dcache-cons(dcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ pcache-cons(pcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ synced(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], icache, pcache) ∧ (asynced1 → synced((files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)], icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
(m ∈ dirs0 ⊃ mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).meta, false, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).nlink, 0, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).size) ) = mkinode(m1, md1, boolvar, m3, m4, m5), dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries1), err = ESUCCESS, afs-cons(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1), false; err, icache); icache_set# (getinode (mkdentry(str, ino0).ino, dirs0[m, (m ∈ dirs0 ⊃ mkdir(m0 + 1, md2, # links(m, dirs0), m2, entries1[str, ino0]);dirs0[m]).meta:= md0], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, icache); dcache_set#(m1, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons(icache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ dcache-cons(dcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ pcache-cons(pcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ synced(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, 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

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(m ∈ dirs0 ⊃ mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .meta, false, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .nlink, 0, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .size) ), m1, md1, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (m ∈ dirs0 ⊃ mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .meta, false, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .nlink, 0, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[m] ) .size) ), m1, md1, boolvar, m3, m4, m5