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Proof step 46 from proof copy-stream-append (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# buf1 = n2 + n1 + m, n0 + m ≤ # buf0 ⊦ ⌜n2⌝ + ⌜m⌝ = #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - m = n; (s)