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Proof step 10 from proof overwrite-write-inode-dirty (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 11:
icache[ino] = mkientry(boolvar, inode), ino ∈ files, ino ∈ icache, ino ∈ icache[ino, mkientry(true, (inode.meta:= md).size:= m)] ⊦ (((files ⊕ pcache) ⊕ icache)[ino].meta:= md).size:= m = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino], inode.directory

Rule argument

fma: ino ∈ icache[ino, mkientry(true, (inode.meta:= md).size:= m)]

Additional information

Used simplifier rules: at-icache-overwrite-not-cached: ⊦ ¬ ino ∈ icache → (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 ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws) Used formulas: ino ∈ icache[ino, mkientry(true, (inode.meta:= md).size:= m)]