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Proof step 358 from proof refine-write_inode (previous step)

cache_files[ino] = mkfile(m8, md4, # links(ino, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino] = mkientry(boolvar0, mkinode(m, md3, false, m4, m5, m7)), 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, ino ∈ cache_files, m3 ∈ cache_icache, ¬ 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), content0 ⊕ mkcontent(m3, cache_pcache)) ;((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] ) = mkfile(m7, md3, m4, content1 ⊕ mkcontent(ino, cache_pcache))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 359:
cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino] = mkientry(boolvar0, mkinode(m, md3, false, m4, m5, m7)), cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), cache_files[ino] = mkfile(m8, md4, # links(ino, cache_dirs), content1), 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), m3 ∈ cache_icache, ino ∈ cache_files, 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), content0 ⊕ mkcontent(m3, cache_pcache)) ;((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] ) = mkfile(m7, md3, m4, content1 ⊕ mkcontent(ino, cache_pcache)), ino = m3

Rule argument

fma: ino = m3

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)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: ino = m3