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Proof step 12 from proof is-encoded-rec-append (previous step)

# buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf = 0, is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), ∀ vtbl0, buf, buf0, v, n. # vtbl0 < # ∅ → # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ∧ is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)) ∧ is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl0, buf) → is-encoded-rec(vtbl0[v, n], buf + buf0) ∨ v ∈ vtbl0 ⊦ buf0 = subarray(buf0, 0, ENCODED_VOLID_SIZE) + subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: encoding-nat-buffer name: subarray-append-consec0 seq: ⊦ n0 + n1 ≤ # buf → subarray(buf, 0, n0) + subarray(buf, n0, n1) = subarray(buf, 0, n0 + n1) subst: [n1, n0, buf] → [ENCODED_NAT_SIZE, ENCODED_VOLID_SIZE, buf0] flags: <all paths>

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: ENCODED_NAT_SIZE, ENCODED_VOLID_SIZE, buf0