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Proof step 32 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + ⌜m⌝ + #(⌜buf1⌝ from n1 + m), n4 < n2, n1 < # buf1, n0 + m ≤ # buf0, n1 + m ≤ # buf1 ⊦ buf1[(n4 + m) + n1] = ⌜buf1⌝ [(n1 + m) + n4], #(⌜buf0⌝ from n0) < ⌜m⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: buffer-inf-conv name: tostream-at seq: ⊦ n < # buf → ⌜buf⌝ [n] = buf[n] subst: [n, buf] → [(n1 + m) + n4, buf1] flags: <all paths>

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% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s) Used terms: (n1 + m) + n4, buf1