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Proof step 338 from proof refine-write_inode (previous step)

cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.directory, 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), ino ∈ cache_files, m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))], ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 339:
cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode = mkinode(m, md3, boolvar0, m4, m5, m7), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), boolvar0, 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[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))], m3 ∈ cache_files, m3 ∈ cache_icache, ino ∈ cache_files, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache [m3, mkientry (true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2)) ] [ino ] .inode, m, md3, boolvar0, m4, m5, m7]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache [m3, mkientry (true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2)) ] [ino ] .inode, m, md3, boolvar0, m4, m5, m7