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Proof step 27 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + ⌜m⌝ + #(⌜buf1⌝ from n1 + m), n1 < # buf1, n3 < n2 + m, m ≤ n3, n1 + m ≤ # buf1, n0 + m ≤ # buf0 ⊦ buf1[n3 + n1] = (⌜buf1⌝ from n1 + m)[n3 - m], n2 = 0, #(⌜buf0⌝ from n0) < ⌜m⌝

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
# buf1 = n2 + n1 + m, n3 = n4 + m, ⌜# buf1⌝ = ⌜n1⌝ + ⌜m⌝ + #(⌜buf1⌝ from n1 + m), n3 < n2 + m, n1 < # buf1, n0 + m ≤ # buf0, n1 + m ≤ # buf1, m ≤ n3 ⊦ buf1[n3 + n1] = (⌜buf1⌝ from n1 + m)[n4], n2 = 0, #(⌜buf0⌝ from n0) < ⌜m⌝

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n3, m, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n3, m, n