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Proof step 6 from proof is-encoded-pad-too-small (previous step)

# buf0 = # ns * ENCODED_NAT_SIZE, # buf0 + # buf1 < ENCODED_NAT_SIZE, is-aligned(# buf0 + # buf1, EB_PAGE_SIZE), is-encoded(ns, buf0) ⊦ # ns = 0, ns = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ # buf < ENCODED_NAT_SIZE → (is-encoded(ns, buf) ↔ ns = ∅ ∧ buf = mkbuf(0))

Rule argument

spec: <toplevel> name: is-encoded-too-small seq: ⊦ # buf < ENCODED_NAT_SIZE → (is-encoded(ns, buf) ↔ ns = ∅ ∧ buf = mkbuf(0)) subst: [buf, ns] → [buf0, ns] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s) Used terms: buf0, ns