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Proof step 30 from proof prepost-encode-orphans (previous step)

is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2 \ orphans, subarray(buf, 0, m0)), m0 + # orphans * ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + # orphans * ENCODED_NAT_SIZE ≤ # buf, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, # buf ≤ LEB_SIZE, orphans ⊆ orphans2 ⊦ # orphans = 0, orphans = ∅, ∃ n. n ∈ orphans

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 32:
is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2 \ orphans, subarray(buf, 0, m0)), # buf ≤ LEB_SIZE, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + # orphans * ENCODED_NAT_SIZE ≤ # buf, m0 + # orphans * ENCODED_NAT_SIZE ≤ LEB_SIZE, orphans ⊆ orphans2 ⊦ # orphans = 0, ∀ n. n ∈ orphans ↔ n ∈ ∅, ∃ n. n ∈ orphans

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [∅, orphans] flags: <all paths>

Additional information

Used terms: ∅, orphans