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Proof step 50 from proof prepost-write-orphans (previous step)

# buf = 0, # buf1 = 0, n < # avol1, ebm-vol-inv(avol1[n, mapped(mkbuf(0))]), ebm-vol-inv(avol1), is-encoded(orphans0, buf1) ⊦ # orphans0 = 0, orphans0 = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ is-encoded(ns, buf) → # buf = # ns * ENCODED_NAT_SIZE

Rule argument

spec: encoding-orphans name: is-encoded-size seq: ⊦ is-encoded(ns, buf) → # buf = # ns * ENCODED_NAT_SIZE subst: [ns, buf] → [orphans0, buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); (s)% ⊦ ENCODED_NAT_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: orphans0, buf1