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Proof step 222 from proof inv-write_inode (previous step)

asynced3 ↔ false, err = ESUCCESS, inode = mkinode(m, md, boolvar, m0, m1, m2), inode0 = mkinode(m, md, boolvar, m0, m1, m2), afs-cons (dirs, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size]), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-write-inode(inode, dirs, files), synced(dirs, icache, pcache), asynced2 → synced(files, icache, pcache), asynced2 ∨ boolvar, m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar ∨ m ∈ files ∧ m0 = files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪icache_get#(inode0.ino, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := inode0.meta; if ¬ inode0.directory then inode1.size := inode0.size; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons (icache, dirs, files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ]) ∧ dcache-cons (dcache, dirs, files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ]) ∧ pcache-cons (pcache, dirs, files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ]) ∧ synced(dirs, icache, pcache) ∧ ( asynced2 → synced (files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ], icache, pcache))), inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 223:
¬ asynced3, err = ESUCCESS, afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪icache_get#(m, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := md; inode1.size := m2; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons(icache, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ dcache-cons(dcache, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ pcache-cons(pcache, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, (files[m].meta:= md).size:= m2], icache, pcache))

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)