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Proof step 19 from proof ls-datasize-zero (previous step)

n ≤ # buf, ∃ buf0. buf = mkempbuf(n) + buf0 ⊦ ∀ n0. n0 < n → buf[n0] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
n0 < n ⊦ (mkempbuf(n) + buf0)[n0] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)