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Proof step 46 from proof fsync-inode-keep-abs (previous step)

dirs[m0] = mkdir(m1, md0, m2, m3, entries), icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ dirs, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))])[ino]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ ino ≠ m → (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino]
Proof step 48:
icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), ino = m, icache-cons(icache, dirs, files), ino ∈ files, m0 ∈ dirs, m ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))])[ino]

Rule argument

spec: <toplevel> name: at-icache-overwrite-other seq: ⊦ ino ≠ m → (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino] subst: [ino, ie, m, icache, files] → [ino, mkientry(false, mkinode(m0, md, true, m2, m3, m1)), m, icache, files ⊕ pcache] flags: <all paths>

Additional information

Used terms: ino, mkientry(false, mkinode(m0, md, true, m2, m3, m1)), m, icache, files ⊕ pcache