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Proof step 8 from proof overwrite-write-inode-clean-dir (previous step)

icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino ∈ dirs, ino ∈ icache ⊦ ∀ ino0. (ino0 ∈ (files ⊕ pcache) ⊕ icache ↔ ino0 ∈ (files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))]) ∧ ( ino0 ∈ (files ⊕ pcache) ⊕ icache → ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))])[ino0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino ∈ icache, ino ∈ dirs, ino0 ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))])[ino0]

Rule argument

Additional information

Used simplifier rules: in-icache-overwrite: ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files;%in-pcache-overwrite: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files;