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Proof step 4 from proof at-icache-overwrite-other (previous step)

⊦ (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino], ino = m, ino ∈ icache[m, ie] ∧ ¬ icache[m, ie][ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ icache[ino].inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)