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

icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))], ino0 ∈ files, ino ∈ dirs, ino ∈ icache, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))])[ino0], ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))] ∧ ¬ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.directory, ino0 ∈ icache, ino ∈ icache, ino ∈ dirs, ino0 ∈ files, ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache))

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-no-file: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino];%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));