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Proof step 9 from proof is-encoded-unique (previous step)

# buf1 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf2 = ENCODED_NAT_SIZE, # buf3 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf4 = ENCODED_NAT_SIZE, buf2 + buf1 + buf0 = buf4 + buf3 + buf, is-encoded(# vtbl1, buf4), is-encoded(# vtbl0, buf2), is-encoded-rec(vtbl1, buf3), is-encoded-rec(vtbl0, buf1) ⊦ vtbl0 = vtbl1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)

Rule argument

spec: array-splice, inst: encoding-nat-buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [buf3 + buf, buf4, buf1 + buf0, buf2] flags: <all paths>

Additional information

Used simplifier rules: is-encoded-rec-unique: ⊦ is-encoded-rec(vtbl0, buf) → (is-encoded-rec(vtbl1, buf) ↔ vtbl0 = vtbl1);% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)%⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2); (ws)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer] Used terms: buf3 + buf, buf4, buf1 + buf0, buf2