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Proof step 2 from proof overwrite-write-inode-clean-file (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
ino ∈ icache, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, icache[ino].inode.nlink, files[ino].content ⊕ mkcontent(ino, pcache))] = (files[ino, (files[ino].meta:= md).size:= m] ⊕ pcache) ⊕ icache[ino, mkientry(false, (icache[ino].inode.meta:= md).size:= m)], icache[ino].inode.directory

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite: ⊦ 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);%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)