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Proof step 140 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(boolvar0, mkinode(m2, md3, boolvar, m3, m6, m10)), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], m ∈ files, m ∈ icache, m1 ∈ files, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files);valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files)) ⊦ m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m3 = (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md3, boolvar, m3, m6, m10) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).meta, false, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink, 0, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(boolvar0, mkinode(m2, md3, boolvar, m3, m6, m10)), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files, ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m3 = (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md3, boolvar, m3, m6, m10) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).meta, false, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink, 0, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ 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)