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Proof step 8 from proof at-icache-overwrite-other (previous step)

icache[ino] = mkientry(boolvar0, mkinode(m0, md, boolvar, m1, m2, m3)) ⊦ (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ boolvar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 10:
icache[ino] = mkientry(boolvar0, mkinode(m0, md, boolvar, m1, m2, m3)) ⊦ (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ boolvar, ino ∈ icache[m, ie] ∧ icache[m, ie][ino].inode.directory

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] → [ino, icache[m, ie], files] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)%⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s) Used terms: ino, icache[m, ie], files