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Proof step 121 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m2, m3, m4)), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files, ino ∈ icache ⊦ m1 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m2 = (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m2, m3, m4) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).meta, false, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).nlink, 0, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 122:
⊦ icache-cons(icache, dirs, 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) ))
Proof step 123:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), icache[ino] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m2, m3, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(dirs, icache, pcache), synced(files, icache, pcache), ino ∈ icache, m ∈ 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)) ⊦ m1 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m2 = (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m2, m3, m4) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).meta, false, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).nlink, 0, (ino = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[ino]).size) ) )

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, 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) )) subst: [icache, dirs, files] → [icache, dirs, files] flags: <all paths>

Additional information

Used terms: icache, dirs, files