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Proof step 7 from proof datasize-subarray0-h (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
subarray(buf, 0, m)[m1] = empty, m1 < m, m1 < # buf, m ≤ # buf, ∀ m, buf. m1 ≤ m ∧ m ≤ # buf ∧ m1 ≤ # buf → datasize(subarray(buf, 0, m), m1) = datasize(buf, m1) ⊦ (buf[m1] = empty ⊃ datasize(subarray(buf, 0, m), m1);m1 + 1) = (buf[m1] = empty ⊃ datasize(buf, m1);m1 + 1)

Rule argument

fma: subarray(buf, 0, m)[m1] = empty

Additional information

Used simplifier rules: ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (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% ⊦ m + n = m + n0 ↔ n = n0; (s) Used formulas: subarray(buf, 0, m)[m1] = empty