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Proof step 56 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, ⌜dx⌝ = ⌜buf1⌝ , m + n1 ≤ # buf1, n0 + m ≤ # buf0 ⊦ n2 = # buf1 - n1 + m, #(⌜buf0⌝ from n0) < ⌜m⌝

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf1, n1 + m, n]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf1, n1 + m, n