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Proof step 526 from proof inv-rename-file-dentry (previous step)

dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] = mkientry(boolvar0, mkinode(m2, md, boolvar, m5, m6, m7)), icache0[ino] = mkientry(boolvar2, mkinode(m8, md4, boolvar1, m9, m10, m11)), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, ino ∈ icache0 → m8 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m9 = files[ino].nlink ∧ m10 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md4, boolvar1, m9, m10, m11) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) ), asynced2 → synced(files, icache0, pcache), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files ∧ icache0[ino0].inode.nlink = files[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files[icache0[ino0].inode.ino].meta, false, files[icache0[ino0].inode.ino].nlink, 0, files[icache0[ino0].inode.ino].size) ) ), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO, ino = entries[str0] ∨ ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] ⊦ entries[str0] ∈ dirs0, m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m5 = (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md, boolvar, m5, m6, m7) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).meta, true, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nlink, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nsubdirs, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).size) ;mkinode (ino, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).meta, false, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink, 0, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).size) ) )

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 527:
icache0[ino] = mkientry(boolvar2, mkinode(m8, md4, boolvar1, m9, m10, m11)), icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] = mkientry(boolvar0, mkinode(m2, md, boolvar, m5, m6, m7)), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), ino ∈ icache0 → m8 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m9 = files[ino].nlink ∧ m10 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md4, boolvar1, m9, m10, m11) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) ), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files ∧ icache0[ino0].inode.nlink = files[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files[icache0[ino0].inode.ino].meta, false, files[icache0[ino0].inode.ino].nlink, 0, files[icache0[ino0].inode.ino].size) ) ), ino = entries[str0] ∨ ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))], links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ino = entries[str0], entries[str0] ∈ dirs0, m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m5 = (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md, boolvar, m5, m6, m7) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).meta, true, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nlink, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nsubdirs, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).size) ;mkinode (ino, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).meta, false, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink, 0, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).size) ) )

Rule argument

fma: ino = entries[str0]

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)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s) Used formulas: ino = entries[str0]