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Proof step 49 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, m ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[m] = ((files ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))])[m]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 51:
icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))][m].inode.directory, icache-cons(icache, dirs, files), m ∈ files, m0 ∈ dirs, m ∈ icache, m ∈ icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))] ⊦ ((files ⊕ pcache) ⊕ icache)[m] = (files ⊕ pcache)[m]

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [m, icache [m, mkientry(false, mkinode(m0, md, true, m2, m3, m1)) ], files ⊕ pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (s)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: m, icache[m, mkientry(false, mkinode(m0, md, true, m2, m3, m1))], files ⊕ pcache