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Proof step 107 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ ino0 = ino, mkfile(icache[ino0].inode.size, icache[ino0].inode.meta, icache[ino0].inode.nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile (icache[ino0].inode.size, icache[ino0].inode.meta, icache[ino0].inode.nlink, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])), icache[ino0].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 108:
icache[ino0].inode = mkinode(m2, md0, boolvar, m3, m4, m5), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ¬ boolvar, ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache[ino0].inode, m2, md0, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[ino0].inode, m2, md0, boolvar, m3, m4, m5