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Proof step 11 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)), ino ∈ files, ino ∈ icache ⊦ ∀ ino0. ( ino0 ∈ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache))] ↔ ino0 ∈ (files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))]) ∧ ( ino0 ∈ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache))] → ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache))][ino0] = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), files[ino] = mkfile(m4, md1, m5, content), ino ∈ icache, ino ∈ files, ino0 ∈ files ⊦ (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

Additional information

Used simplifier rules: in-icache-overwrite: ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files;%in-pcache-overwrite: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files;% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)