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Proof step 135 from proof inv-write_inode (previous step)

dirs[m1] = mkdir(m0, md0, # links(m1, dirs), m2, entries), icache[m1] = mkientry(false, mkinode(m1, md0, true, # links(m1, dirs), m2, m0)), icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, dirs), m2, m0))][ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), afs-cons(dirs, files), afs-cons(dirs[m1, mkdir(m0, md, # links(m1, dirs), m2, entries)], files), synced(dirs, icache, pcache), m1 ∈ dirs, m1 ∈ icache, ino ∈ icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, dirs), m2, m0))], asynced2 → synced(files, icache, pcache), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (ino ∈ dirs ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).meta, true, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).nlink, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 136:
icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, dirs), m2, m0))][ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), icache[m1] = mkientry(false, mkinode(m1, md0, true, # links(m1, dirs), m2, m0)), dirs[m1] = mkdir(m0, md0, # links(m1, dirs), m2, entries), afs-cons(dirs[m1, mkdir(m0, md, # links(m1, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, dirs), m2, m0))], m1 ∈ icache, m1 ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ino = m1, m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (ino ∈ dirs ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).meta, true, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).nlink, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

fma: ino = m1

Additional information

Used simplifier rules: ⊦ icache[ino, ie][ino] = ie; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ ino ∈ icache[ino, ie]; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s) Used formulas: ino = m1