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Proof step 21 from proof is-encoded-rec-unique (previous step)

# buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # buf4 = ENCODED_VOLID_SIZE, # buf3 = ENCODED_NAT_SIZE, # buf = (# vtbl1 - 1) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl + 1 = # vtbl1, ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), buf2 + buf1 + buf0 = buf4 + buf3 + buf, is-encoded(v0, buf2), is-encoded(vtbl[v, n][v0], buf1), is-encoded(vtbl1[v1], buf3), is-encoded(v1, buf4), is-encoded-rec(vtbl[v, n] -- v0, buf0), is-encoded-rec(vtbl1 -- v1, buf), v0 ∈ vtbl[v, n], v1 ∈ vtbl1, ∀ vtbl2, buf, vtbl1. # vtbl2 < # vtbl[v, n] → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl2, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl2 = vtbl1 ⊦ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl[v, n] = vtbl1, vtbl1 = ∅, v ∈ vtbl

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# buf = m * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = ENCODED_NAT_SIZE, # buf4 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, # buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m + 1, buf2 + buf1 + buf0 = buf4 + buf3 + buf, ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl + 1 = # vtbl1, is-encoded(v1, buf4), is-encoded(vtbl1[v1], buf3), is-encoded(vtbl[v, n][v0], buf1), is-encoded(v0, buf2), is-encoded-rec(vtbl1 -- v1, buf), is-encoded-rec(vtbl[v, n] -- v0, buf0), v1 ∈ vtbl1, v0 ∈ vtbl[v, n], ∀ vtbl2, buf, vtbl1. # vtbl2 < # vtbl[v, n] → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl2, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl2 = vtbl1 ⊦ # vtbl1 = 0, ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl[v, n] = vtbl1, vtbl1 = ∅, v ∈ vtbl

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# vtbl1, m]

Additional information

Used simplifier rules: ⊦ # vtbl = 0 ↔ vtbl = ∅; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # vtbl1, m