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Proof step 33 from proof encode (previous step)

# buf = # buf4, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) < ENCODED_VOLID_SIZE, # buf3 < ENCODED_VOLID_SIZE, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, v0 ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf3, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ v ∈ vtbl, v0 ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ v ∈ vtbl ↔ (∃ n, vtbl0. vtbl = vtbl0[v, n] ∧ ¬ v ∈ vtbl0)

Rule argument

spec: store, inst: vtbl name: exin seq: ⊦ v ∈ vtbl ↔ (∃ n, vtbl0. vtbl = vtbl0[v, n] ∧ ¬ v ∈ vtbl0) subst: [vtbl, v] → [vtbl1, v0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ ¬ m + n < m; (s) Used terms: vtbl1, v0