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Proof step 116 from proof encode (previous step)

# buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, # buf11 = 0, # buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, # buf10 = 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE = # buf5, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_VOLID_SIZE ≤ # buf9, m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, vtbl1 -- v ⊥ vtbl[v, vtbl1[v]]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store-union, inst: vtbl name: disjoint seq: ⊦ vtbl ⊥ vtbl0 ↔ (∀ v. ¬ v ∈ vtbl ∨ ¬ v ∈ vtbl0) subst: [vtbl0, vtbl] → [vtbl[v, vtbl1[v]], vtbl1 -- v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ vtbl -- v0 ↔ v ≠ v0 ∧ v ∈ vtbl; (s)% ⊦ v ≠ v0 → (v ∈ vtbl[v0, n] ↔ v ∈ vtbl); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%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%disjoint-in-right: ⊦ v ∈ vtbl ∧ vtbl0 ⊥ vtbl → ¬ v ∈ vtbl0; (forward) from specification store-union[vtbl]%disjoint-in-left: ⊦ v ∈ vtbl ∧ vtbl ⊥ vtbl0 → ¬ v ∈ vtbl0; (forward) from specification store-union[vtbl]% ⊦ m < n → n ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid] Used terms: vtbl[v, vtbl1[v]], vtbl1 -- v