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Proof step 1 from proof inos-write (conclusion)

⊦ ri[key, adr].inos = ri.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 3:
⊦ ∀ n. n ∈ ri[key, adr].inos ↔ n ∈ ri.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅)

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [ri.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅), ri[key, adr].inos] flags: <all paths>

Additional information

Used terms: ri.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅), ri[key, adr].inos