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Proof step 322 from proof inv-write_inode (previous step)

icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))][ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, ino ∈ icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))] ⊦ m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).meta, false, (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).nlink, 0, (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 323:
⊦ 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 324:
icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))][ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), ino ∈ icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))], m ∈ files, m ∈ icache, ∀ 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)) ⊦ m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).meta, false, (ino = m ⊃ (files[m].meta:= md).size:= m2;files[ino]).nlink, 0, (ino = m ⊃ (files[m].meta:= md).size:= m2;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