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Proof step 230 from proof refine-write_inode (previous step)

(ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]) = mkfile(m6, md2, m7, content0), (∅)[ino] = mkientry(boolvar0, mkinode(m1, md1, boolvar, m3, m4, m5)), cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), 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, ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache)) ;mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) ) = mkfile(m6, md2, m7, content0 ⊕ mkcontent(ino, cache_pcache)), m ∈ cache_icache, ino ∈ cache_icache

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = m

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: ino = m