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Proof step 20 from proof overwrite-write-inode-clean-dir (previous step)

files[ino0] = mkfile(m7, md2, m8, content), icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0] = mkientry(boolvar0, mkinode(m3, md1, true, m4, m5, m6)), icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino0 = ino, ino0 ∈ icache, ino ∈ icache, ino ∈ dirs, ino0 ∈ files, ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m7, md2, m8, content ⊕ mkcontent(ino0, pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), files[ino] = mkfile(m7, md2, m8, content), ino ∈ icache, ino ∈ dirs, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m7, md2, m8, content ⊕ mkcontent(ino, pcache))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (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)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)