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Proof step 36 from proof inv-iget (previous step)

(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) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ icache-cons(icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], dirs, files), ino ∈ icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ 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 38:
(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) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, ∀ ino. ino ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))] → icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].inode.ino = ino ∧ (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].dirty ⊃ valid-file-inode(icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, 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 [m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2)) ], dirs, files] flags: <all paths>

Additional information

Used terms: icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], dirs, files