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Proof step 14 from proof is-encoded-rec-size (previous step)

# buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, is-encoded(v0, buf2), is-encoded(vtbl0[v, n][v0], buf1), is-encoded-rec(vtbl0[v, n] -- v0, buf0), v0 ∈ vtbl0[v, n], ∀ vtbl1, buf. # vtbl1 < # vtbl0[v, n] → is-encoded-rec(vtbl1, buf) → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ⊦ # buf0 = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl0, v ∈ vtbl0

User applied rule apply induction

And closed the goal!

Rule argument

subst: [vtbl1, buf] → [vtbl0[v, n] -- v0, buf0]

Additional information

Used simplifier rules: ⊦ v ∈ vtbl → #(vtbl -- v) = (# vtbl)-1; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ (m + 1)-1 = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s) Used terms: vtbl0[v, n] -- v0, buf0