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Proof step 13 from proof overwrite-write-inode-clean-file (previous step)

files[ino] = mkfile(m4, md1, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), ino0 ∈ files, ino ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ (ino0 = ino ⊃ mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache));((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 14:
icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), files[ino] = mkfile(m4, md1, m5, content), ino0 ∈ icache, ino ∈ icache, ino ∈ files, ino0 ∈ files, ino0 ∈ icache[ino, mkientry(true, mkinode(m0, md, false, m1, m2, m))] ⊦ (ino0 = ino ⊃ mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache));((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0]

Rule argument

fma: ino0 ∈ icache[ino, mkientry(true, mkinode(m0, md, false, m1, m2, m))]

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws) Used formulas: ino0 ∈ icache[ino, mkientry(true, mkinode(m0, md, false, m1, m2, m))]