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Proof step 23 from proof overwrite-write-inode-dirty (previous step)

icache[ino] = mkientry(boolvar, inode), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], ino0 = ino, inode.directory, ino0 ∈ icache[ino, mkientry(true, (inode.meta:= md).size:= m)] ∧ ¬ icache[ino, mkientry(true, (inode.meta:= md).size:= m)][ino0].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
icache[ino] = mkientry(boolvar, inode), icache[ino0].inode.directory, ino ∈ icache, ino ∈ files, ino0 ∈ files, ino0 ∈ icache ⊦ ino0 = ino, mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], inode.directory

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));% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)