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Proof step 38 from proof inv-iget (previous step)

(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) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, ∀ ino. ino ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))] → icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].inode.ino = ino ∧ (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].dirty ⊃ valid-file-inode(icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].inode, dirs, files) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
(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) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino0 ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino = ino0 ∧ (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].dirty ⊃ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino ∈ files ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.nlink = files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.nsubdirs = 0 ∧ ¬ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode = (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino ∈ dirs ⊃ mkinode (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].meta, true, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nsubdirs, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].size) ;mkinode (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].meta, false, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink, 0, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.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)