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Proof step 417 from proof refine-write_inode (previous step)

cache_icache[m] = mkientry(boolvar, mkinode(m0, md, false, m1, m3, m4)), cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), 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_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ cache_icache[ino].inode.ino ∈ cache_files ∧ cache_icache[ino].inode.nlink = cache_files[cache_icache[ino].inode.ino].nlink ∧ cache_icache[ino].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino].inode.directory ; (ino ∈ cache_dirs ∨ ino ∈ cache_files) ∧ cache_icache[ino].inode = (cache_icache[ino].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino].inode.ino, cache_dirs[cache_icache[ino].inode.ino].meta, true, cache_dirs[cache_icache[ino].inode.ino].nlink, cache_dirs[cache_icache[ino].inode.ino].nsubdirs, cache_dirs[cache_icache[ino].inode.ino].size) ;mkinode (cache_icache[ino].inode.ino, cache_files[cache_icache[ino].inode.ino].meta, false, cache_files[cache_icache[ino].inode.ino].nlink, 0, cache_files[cache_icache[ino].inode.ino].size) ) ) ⊦ m1 = # links(m, cache_dirs)

User applied rule all left

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws) Used terms: m