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Proof step 70 from proof refine-write_inode (previous step)

cache_icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, cache_dirs), m6, m0))][ino] = mkientry(boolvar, mkinode(m, md0, true, m2, m3, m4)), cache_dirs[m1] = mkdir(m0, md2, # links(m1, cache_dirs), m6, entries0), cache_icache[m1] = mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m6, m0)), cache_files[ino] = mkfile(m5, md1, # links(ino, cache_dirs), content), 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), ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md, true, # links(m1, cache_dirs), m6, m0))], m1 ∈ cache_dirs, m1 ∈ cache_icache, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino0. ino0 ∈ cache_icache → cache_icache[ino0].inode.ino = ino0 ∧ (cache_icache[ino0].dirty ⊃ cache_icache[ino0].inode.ino ∈ cache_files ∧ cache_icache[ino0].inode.nlink = cache_files[cache_icache[ino0].inode.ino].nlink ∧ cache_icache[ino0].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino0].inode.directory ; (ino0 ∈ cache_dirs ∨ ino0 ∈ cache_files) ∧ cache_icache[ino0].inode = (cache_icache[ino0].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino0].inode.ino, cache_dirs[cache_icache[ino0].inode.ino].meta, true, cache_dirs[cache_icache[ino0].inode.ino].nlink, cache_dirs[cache_icache[ino0].inode.ino].nsubdirs, cache_dirs[cache_icache[ino0].inode.ino].size) ;mkinode (cache_icache[ino0].inode.ino, cache_files[cache_icache[ino0].inode.ino].meta, false, cache_files[cache_icache[ino0].inode.ino].nlink, 0, cache_files[cache_icache[ino0].inode.ino].size) ) ) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(m5, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: ino = m1

Additional information

Used simplifier rules: ⊦ icache[ino, ie][ino] = ie; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)%⊦ 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)% ⊦ ino ∈ icache[ino, ie]; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s) Used formulas: ino = m1