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Proof step 21 from proof encode (previous step)

# buf1 = n0 + ENCODED_NAT_SIZE, # buf = n0 + ENCODED_NAT_SIZE, is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)), # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ n0 ⊦ buf1 = subarray(buf1, 0, ENCODED_NAT_SIZE) + subarray(buf1, ENCODED_NAT_SIZE, n0)

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] → [n0, ENCODED_NAT_SIZE, buf1] 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 = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 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 < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)% ⊦ buf + buf0 = buf ↔ # buf0 = 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ m < n → ¬ n < m; (s) Used terms: n0, ENCODED_NAT_SIZE, buf1