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Proof step 23 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 ∈ 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)), ino0 = ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
files[ino0] = mkfile(m7, md2, m8, content), icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), icache[ino0] = mkientry(boolvar0, mkinode(m3, md1, true, m4, m5, m6)), ino0 ∈ files, ino ∈ dirs, ino ∈ icache, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m7, md2, m8, content ⊕ mkcontent(ino0, pcache)), ino0 = ino

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)