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Proof step 465 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache ⊦ icache-cons(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], dirs, files)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 466:
⊦ 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 467:
icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ ∀ ino. ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, 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 [m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2)) ], dirs, files] flags: <all paths>

Additional information

Used terms: icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], dirs, files