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Proof step 48 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), datakey(ino, n) ∈ pcache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino ∈ files, ino ∈ icache ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], n = m, n ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 50:
icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino ∈ files, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino, n) ∈ pcache, n ∈ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]) ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])[n], n = m, n ∈ content0

Rule argument

spec: <toplevel> name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n, mkcontent (ino, pcache[datakey(ino, m), mkpentry(false, buf)]), content0[m, buf]] flags: <all paths>

Additional information

Used simplifier rules: at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ n ≠ n0 → content[n0, buf][n] = content[n]; (s)% ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws) Used terms: n, mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]), content0[m, buf]