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Proof step 29 from proof is-encoded-rec-unique (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# 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

Rule argument

Additional information

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