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

icache[ino].inode = mkinode(m0, md, true, m1, m2, m3), ino ∈ icache, ino ∈ files ⊦ (files[ino].content ⊕ mkcontent(ino, pcache))[m, buf] = files[ino].content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
icache[ino] = mkientry(boolvar, inode), inode = mkinode(m0, md, true, m1, m2, m3), ino ∈ files, ino ∈ icache ⊦ (files[ino].content ⊕ mkcontent(ino, pcache))[m, buf] = files[ino].content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar, inode