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Proof step 50 from proof inv-fsync (previous step)

files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files1[m0] = mkfile(m4, md, # links(m0, dirs0), content2), afs-cons(dirs1, files2), afs-cons(dirs1, files0), afs-cons(dirs0, files1), dcache-cons(dcache, dirs1, files2), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs0, files1), icache-cons(icache, dirs1, files2), icache-cons(icache, dirs1, files0), pcache-cons(pcache, dirs1, files2), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache0, dirs0, files1), synced(dirs1, icache, pcache), synced(dirs1, icache, pcache0), synced(dirs0, icache0, pcache0), m ∈ files0, m ∈ files2, m0 ∈ files1, ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ valid-file-inode(icache0[ino].inode, dirs0, files1) ;valid-ino(ino, dirs0, files1) ∧ valid-inode(icache0[ino].inode, dirs0, files1) ) ⊦ ∃ err0. ⌊err0⌋ ∨ err0 = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
files1[m0] = mkfile(m4, md, # links(m0, dirs0), content2), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), afs-cons(dirs0, files1), afs-cons(dirs1, files0), afs-cons(dirs1, files2), dcache-cons(dcache, dirs0, files1), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs1, files2), icache-cons(icache, dirs1, files0), icache-cons(icache, dirs1, files2), pcache-cons(pcache0, dirs0, files1), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache, dirs1, files2), synced(dirs0, icache0, pcache0), synced(dirs1, icache, pcache0), synced(dirs1, icache, pcache), m0 ∈ files1, m ∈ files2, m ∈ files0, ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ icache0[ino].inode.ino ∈ files1 ∧ icache0[ino].inode.nlink = files1[icache0[ino].inode.ino].nlink ∧ icache0[ino].inode.nsubdirs = 0 ∧ ¬ icache0[ino].inode.directory ; (ino ∈ dirs0 ∨ ino ∈ files1) ∧ icache0[ino].inode = (icache0[ino].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino].inode.ino, dirs0[icache0[ino].inode.ino].meta, true, dirs0[icache0[ino].inode.ino].nlink, dirs0[icache0[ino].inode.ino].nsubdirs, dirs0[icache0[ino].inode.ino].size) ;mkinode (icache0[ino].inode.ino, files1[icache0[ino].inode.ino].meta, false, files1[icache0[ino].inode.ino].nlink, 0, files1[icache0[ino].inode.ino].size) ) ) ⊦ ∃ err0. ⌊err0⌋ ∨ err0 = ESUCCESS

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)