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Proof step 6 from proof is-encoded-rec-unique (previous step)

# buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), vtbl0 = ∅, is-encoded-rec(vtbl0, buf), is-encoded-rec(vtbl1, buf), ∀ vtbl, buf, vtbl1. # vtbl < # vtbl0 → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl = vtbl1 ⊦ vtbl0 = vtbl1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# buf = 0, 0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded-rec(vtbl1, buf), ∀ vtbl, buf, vtbl1. # vtbl < # ∅ → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl = vtbl1 ⊦ ∅ = vtbl1

Rule argument

Additional information

Used simplifier rules: is-encoded-base: ⊦ is-encoded-rec(∅, buf) ↔ # buf = 0;%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 0 * n = 0; (s)% ⊦ # ∅ = 0; (s)