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Proof step 78 from proof fsync-inode-keep-abs (previous step)

icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), 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], ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))] ∧ ¬ boolvar

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 79:
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

Rule argument

fma: ino = m

Additional information

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