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Proof step 12 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino, icache[ino, mkientry(true, (inode.meta:= md).size:= m)], files ⊕ pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (s)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ (inode.size:= m2).directory ↔ inode.directory; (s)% ⊦ (inode.meta:= md).directory ↔ inode.directory; (s) Used terms: ino, icache[ino, mkientry(true, (inode.meta:= md).size:= m)], files ⊕ pcache