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Proof step 72 from proof fsync-inode-keep-abs (previous step)

icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), icache-cons(icache, dirs, files), m0 ∈ files, m ∈ icache ⊦ ∀ ino. ( ino ∈ (files ⊕ pcache) ⊕ icache ↔ ino ∈ (files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))]) ∧ ( ino ∈ (files ⊕ pcache) ⊕ icache → ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))])[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ files, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))])[ino]

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)