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Proof step 18 from proof prepost-encode-lpt (previous step)

# lpt = n1 + n0, lptsize(n1 + n0, LEB_SIZE) < n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE, is-encoded(lpt, buf, n0) ⊦ n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: encoding-lpt name: lptsize-ge-min seq: ⊦ m ≤ mainareasize * ENCODED_LPROPS_SIZE → ¬ lptsize(mainareasize, LEB_SIZE) < m subst: [m, mainareasize] → [n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE, n1 + n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m * n + n ≤ m1 * n ↔ m + 1 ≤ m1 ∨ n = 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ENCODED_LPROPS_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s) Used terms: n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE, n1 + n0