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Proof step 87 from proof decode (previous step)

is-encoded(vtbl0, buf), is-encoded(# vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl = vtbl0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: is-encoded seq: ⊦ is-encoded(vtbl, buf) ↔ (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl, buf1)) subst: [buf, vtbl] → [buf, vtbl0] flags: <all paths>

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);%is-encoded-rec-unique: ⊦ is-encoded-rec(vtbl0, buf) → (is-encoded-rec(vtbl1, buf) ↔ vtbl0 = vtbl1);% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m - m = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: buf, vtbl0