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Proof step 38 from proof datasize-append-empty-h (previous step)

buf0[m0] = empty, m0 + 1 < # buf0, m0 < # buf0 + # buf1, ∀ buf0, buf1. m0 ≤ # buf0 + # buf1 ∧ (# buf0 ≤ m0 → datasize(buf1, m0 - # buf0) = 0) → datasize(buf0 + buf1, m0) = datasize(buf0, min(m0, # buf0)) ⊦ m0 + 1 = datasize(buf0, m0), (buf0 + buf1)[m0] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-at1 seq: ⊦ n < # buf → (buf + buf0)[n] = buf[n] subst: [n, buf0, buf] → [m0, buf1, buf0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m0, buf1, buf0