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Proof step 447 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, m0 ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode.ino = m0 ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode, dirs, files) ;valid-ino(m0, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode, dirs, files) ), ∀ ino. ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ) ⊦ synced(dirs, icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 448:
icache[m] = mkientry(boolvar, mkinode(m0, md0, false, files[m0].nlink, 0, m4)), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ files, m ∈ files, m ∈ icache, ∀ ino. ino ∈ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))] → icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].dirty ⊃ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino ∈ files ∧ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.nlink = files[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].nlink ∧ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode = (icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino, dirs[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].meta, true, dirs[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].nlink, dirs[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].nsubdirs, dirs[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].size) ;mkinode (icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino, files[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].meta, false, files[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].nlink, 0, files[icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))][ino].inode.ino].size) ) ) ⊦ synced(dirs, icache[m0, mkientry(true, mkinode(m0, md, false, files[m0].nlink, 0, m2))], pcache)

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino, ie]; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (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)