[Imprint][Data Privacy Statement][E-Mail]

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Proof step 176 from proof inv-create (previous step)

icache0[ino] = mkientry(boolvar2, mkinode(m6, md3, boolvar1, m7, m8, m9)), icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] [ino ] = mkientry(boolvar0, mkinode(m, md0, boolvar, m2, m3, m5)), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), 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, ∅)]), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ino ∈ icache0 → m6 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md3, boolvar1, m7, m8, m9) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), ino = ino0 ∨ ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))], links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = ino0, ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, m = ino ∧ (boolvar0 ⊃ (ino = ino0 ∨ ino ∈ files0) ∧ m2 = (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino = ino0 ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m2, m3, m5) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).meta, true, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nlink, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).size) ;mkinode (ino, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).meta, false, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink, 0, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 177:
icache0[ino] = mkientry(boolvar2, mkinode(m6, md3, boolvar1, m7, m8, m9)), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino] = mkientry(boolvar0, mkinode(m, md0, boolvar, m2, m3, m5)), 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), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))], ino ∈ icache0 → m6 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md3, boolvar1, m7, m8, m9) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), asynced1 → synced(files0, icache0, pcache), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = ino0, ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m2 = files0[ino].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m2, m3, m5) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).meta, true, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nlink, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).size) ;mkinode(ino, (files0 ++ ino0)[ino].meta, false, (files0 ++ ino0)[ino].nlink, 0, (files0 ++ ino0)[ino].size) ) )

Rule argument

Additional information

Used simplifier rules: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]; (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)