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Proof step 35 from proof prepost-encode-orphans (previous step)

is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2, subarray(buf, 0, m0)), # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, # buf ≤ LEB_SIZE, m0 ≤ # buf, m0 ≤ LEB_SIZE ⊦ is-encoded-pad(orphans2, # orphans2, buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ is-encoded-pad(ns, n, buf) ↔ n = # ns ∧ (∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(ns, buf0))
Proof step 37:
is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2, subarray(buf, 0, m0)), m0 ≤ LEB_SIZE, m0 ≤ # buf, # buf ≤ LEB_SIZE, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE ⊦ # orphans2 = # orphans2 ∧ (∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(orphans2, buf0))

Rule argument

spec: encoding-orphans name: is-encoded-pad seq: ⊦ is-encoded-pad(ns, n, buf) ↔ n = # ns ∧ (∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(ns, buf0)) subst: [buf, n, ns] → [buf, # orphans2, orphans2] flags: <all paths>

Additional information

Used terms: buf, # orphans2, orphans2