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Proof step 20 from proof overwrite-write-page-clean (previous step)

icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), 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)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 22:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), ino ∈ files, ino ∈ icache ⊦ m2 = m2 ∧ md0 = md0 ∧ m3 = m3 ∧ (content0 ⊕ mkcontent(ino, pcache))[m, buf] = content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [content0, m2, md0, m1, content, m0, md, m] → [ content0[m, buf] ⊕ mkcontent (ino, pcache[datakey(ino, m), mkpentry(false, buf)]), m3, md0, m2, (content0 ⊕ mkcontent(ino, pcache))[m, buf], m3, md0, m2] flags: <all paths>

Additional information

Used terms: content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]), m3, md0, m2, (content0 ⊕ mkcontent(ino, pcache))[m, buf], m3, md0, m2