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Proof step 6 from proof inv-write_inode (previous step)

asynced1 ↔ asynced0, asynced2 ↔ asynced, inode = mkinode(m, md, boolvar, m0, m1, m2), inode0 = inode, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-write-inode(inode0, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar ∨ m ∈ files ∧ m0 = files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪let asynced0 = true, inode = ?, asynced = false in {if asynced2 ∨ inode0.directory then {afs_write_inode#(inode0; err, dirs, files; asynced1); asynced0 := false} else err := ESUCCESS; if err = ESUCCESS then icache_get#(inode0.ino, icache; asynced, inode, err); if err = ESUCCESS ∧ asynced then {inode.meta := inode0.meta; if ¬ inode0.directory then inode.size := inode0.size; icache_set#(inode, asynced0; err, icache)} else if asynced0 then err := EFAIL}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar ∨ m ∈ files ∧ m0 = files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪let asynced0 = true, inode1 = ?, asynced3 = false in {inode := mkinode(m, md, boolvar, m0, m1, m2); if asynced ∨ inode.directory then {afs_write_inode#(inode; err, dirs, files; asynced1); asynced0 := false} else err := ESUCCESS; if err = ESUCCESS then icache_get#(inode.ino, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := inode.meta; if ¬ inode.directory then inode1.size := inode.size; icache_set#(inode1, asynced0; err, icache)} else if asynced0 then err := EFAIL}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ 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).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)