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Proof step 79 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[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), icache-cons(icache, dirs, files), ino ∈ files, m0 ∈ files, m ∈ 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], ino = m, ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))] ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), icache[ino] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ files, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ boolvar

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-other: ⊦ ino ≠ m → (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino];% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)