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Proof step 3 from proof datasize-add-empty-h (previous step)

subarray(buf, n0, n1) = mkempbuf(n1), n0 + n1 ≤ # buf ⊦ datasize(buf, n0 + n1) = datasize(buf, n0)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
subarray(buf, n0, n +1) = mkempbuf(n +1), n0 + n +1 ≤ # buf, ∀ buf, n0. subarray(buf, n0, n) = mkempbuf(n) ∧ n0 + n ≤ # buf → datasize(buf, n0 + n) = datasize(buf, n0) ⊦ datasize(buf, n0 + n +1) = datasize(buf, n0)

Rule argument

indvar: n1

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic