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Proof step 16 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), icache[ino].inode.directory, ino ∈ icache, ino ∈ files ⊦ mkfile(m2, md0, m3, (content0 ⊕ mkcontent(ino, pcache))[m, buf]) = mkfile(m2, md0, m3, content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
icache[ino].inode = mkinode(m0, md, boolvar, m1, m4, m5), files[ino] = mkfile(m2, md0, m3, content0), boolvar, ino ∈ files, ino ∈ icache ⊦ mkfile(m2, md0, m3, (content0 ⊕ mkcontent(ino, pcache))[m, buf]) = mkfile(m2, md0, m3, content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, 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[ino].inode, m0, md, boolvar, m1, 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[ino].inode, m0, md, boolvar, m1, m4, m5