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Proof step 30 from proof is-encoded-rec-unique (previous step)

# buf4 = ENCODED_VOLID_SIZE, # buf3 = ENCODED_NAT_SIZE, # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = # vtbl + 1, vtbl1[v0] = vtbl[v, n][v0], is-encoded(vtbl1[v0], buf3), is-encoded(v0, buf4), is-encoded-rec(vtbl[v, n] -- v0, buf), is-encoded-rec(vtbl1 -- v0, buf), v0 ∈ vtbl[v, n], v0 ∈ 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 ⊦ # buf = (# vtbl1 - 1) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl[v, n] = vtbl1, vtbl1 = ∅, v ∈ vtbl

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # vtbl1, m