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Proof step 123 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ icache-cons(icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 124:
⊦ 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 125:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, m ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ ∀ ino. ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))] → icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino].inode.ino = ino ∧ (icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino].dirty ⊃ valid-file-inode (icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino].inode, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ; valid-ino(ino, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ valid-inode (icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino].inode, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) )

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 [m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5)) ], dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files] flags: <all paths>

Additional information

Used terms: icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files