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Proof step 37 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), v0 ∈ vtbl1, v0 ∈ vtbl[v, n], ∀ v1. (v1 ∈ vtbl[v, n] -- v0 ↔ v1 ∈ vtbl1 -- v0) ∧ (vtbl[v, n] -- v0)[v1] = (vtbl1 -- v0)[v1], ∀ 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, vtbl1 = ∅, v ∈ vtbl, (v1 ∈ vtbl[v, n] ↔ v1 ∈ vtbl1) ∧ vtbl[v, n][v1] = vtbl1[v1]

User applied rule all left

And obtained the following new goals

Proof step 38:
# buf4 = ENCODED_VOLID_SIZE, # buf3 = ENCODED_NAT_SIZE, # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = # vtbl + 1, v1 ∈ vtbl[v, n] -- v0 ↔ v1 ∈ vtbl1 -- v0, vtbl1[v0] = vtbl[v, n][v0], (vtbl[v, n] -- v0)[v1] = (vtbl1 -- v0)[v1], is-encoded(vtbl1[v0], buf3), is-encoded(v0, buf4), 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 ⊦ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl1 = ∅, v ∈ vtbl, (v1 ∈ vtbl[v, n] ↔ v1 ∈ vtbl1) ∧ vtbl[v, n][v1] = vtbl1[v1]

Rule argument

pos: left 11 terms: v1 abort: F discard: T computed: F

Additional information

Used terms: v1