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Proof step 43 from proof inv-format (previous step)

⊦ icache-cons(∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [icache, dirs, files] → [∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ ∅; (s) Used terms: ∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅