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Proof step 8 from proof datasize-subarray-h (previous step)

m0 + m1 = # buf, m2 < m1, ∀ m0, m1, buf. m0 + m1 = # buf ∧ m2 ≤ m1 → datasize(subarray(buf, m0, m1), m2) = (datasize(buf, m0 + m2) ≤ m0 ⊃ 0;datasize(buf, m0 + m2) - m0) ⊦ (buf[m0 + m2] = empty ⊃ datasize(subarray(buf, m0, m1), m2);m2 + 1) = ((buf[m0 + m2] = empty ⊃ datasize(buf, m0 + m2);(m0 + m2) + 1) ≤ m0 ⊃ 0;(buf[m0 + m2] = empty ⊃ datasize(buf, m0 + m2);(m0 + m2) + 1) - m0)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 9:
m0 + m1 = # buf, buf[m0 + m2] = empty, m2 < m1, ∀ m0, m1, buf. m0 + m1 = # buf ∧ m2 ≤ m1 → datasize(subarray(buf, m0, m1), m2) = (datasize(buf, m0 + m2) ≤ m0 ⊃ 0;datasize(buf, m0 + m2) - m0) ⊦ datasize(subarray(buf, m0, m1), m2) = ((buf[m0 + m2] = empty ⊃ datasize(buf, m0 + m2);(m0 + m2) + 1) ≤ m0 ⊃ 0;(buf[m0 + m2] = empty ⊃ datasize(buf, m0 + m2);(m0 + m2) + 1) - m0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n - m = n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)