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Proof step 264 from proof inv-rename-dir-negdentry (previous step)

(m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries4), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), icache0[ino] = mkientry(boolvar2, mkinode(m20, md8, boolvar1, m21, m22, m23)), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m10, entries3), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][ino] = mkientry(boolvar0, mkinode(m16, md7, boolvar, m17, m18, m19)), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), m9 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries0[str] ∈ dirs0, ino ∈ icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))], ino ∈ icache0 → m20 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m21 = files[ino].nlink ∧ m22 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md8, boolvar1, m21, m22, m23) = (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), m = m9 → md4 = md0, ∀ 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(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = m, str0 ∈ entries3, m16 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m17 = files[ino].nlink ∧ m18 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar, m17, m18, m19) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m9 ⊃ mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str);dirs0[ino]).meta, true, (ino = m9 ⊃ mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str);dirs0[ino]).nlink, (ino = m9 ⊃ mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str);dirs0[ino]).nsubdirs, (ino = m9 ⊃ mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str);dirs0[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = m9

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (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)% ⊦ icache[ino, ie][ino] = ie; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ino ∈ icache[ino, ie]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (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 = m9