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Proof step 154 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m ∈ cache_icache, ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ( (cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content0)] ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, boolvar0, m4, m5, m2))] )[ino ]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 155:
⊦ 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 156:
cache_icache[m] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ valid-file-inode(cache_icache[ino].inode, cache_dirs, cache_files) ;valid-ino(ino, cache_dirs, cache_files) ∧ valid-inode(cache_icache[ino].inode, cache_dirs, cache_files) ) ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ( (cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content0)] ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, boolvar0, m4, m5, m2))] )[ino ]

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: [files, dirs, icache] → [cache_files, cache_dirs, cache_icache] flags: <all paths>

Additional information

Used terms: cache_files, cache_dirs, cache_icache