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Proof step 324 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), 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) ) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m2, md, # links(m, cache_dirs), content)] = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))]

User applied rule all left

And obtained the following new goals

Proof step 325:
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), m ∈ cache_files, m ∈ cache_icache, m ∈ cache_icache → cache_icache[m].inode.ino = m ∧ (cache_icache[m].dirty ⊃ valid-file-inode(cache_icache[m].inode, cache_dirs, cache_files) ;valid-ino(m, cache_dirs, cache_files) ∧ valid-inode(cache_icache[m].inode, cache_dirs, cache_files) ) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m2, md, # links(m, cache_dirs), content)] = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))]

Rule argument

pos: left 11 terms: m abort: F discard: T computed: T

Additional information

Used terms: m