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Proof step 5 from proof is-encoded-rec-unique (previous step)

# buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded-rec(vtbl1, buf), is-encoded-rec(vtbl0, 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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
# 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
Proof step 9:
# buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), 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, vtbl0 = ∅

Rule argument

fma: vtbl0 = ∅

Additional information

Used formulas: vtbl0 = ∅