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Proof step 32 from proof overwrite-write-inode-dirty (previous step)

icache[ino] = mkientry(boolvar, inode), ino ∈ icache, ino ∈ files, ino0 ∈ files ⊦ 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, ino0 ∈ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
icache[ino] = mkientry(boolvar, inode), files[ino0] = mkfile(m0, md0, m1, content), ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ mkfile(m0, md0, m1, content ⊕ mkcontent(ino0, pcache)) = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], inode.directory, ino0 ∈ icache

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[ino0], m0, md0, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[ino0], m0, md0, m1, content