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Proof step 3 from proof datasize-subarray-h (previous step)

m0 + m1 = # buf, m ≤ m1 ⊦ datasize(subarray(buf, m0, m1), m) = (datasize(buf, m0 + m) ≤ m0 ⊃ 0;datasize(buf, m0 + m) - m0)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
⊦ datasize(buf, 0) = 0
Proof step 5:
⊦ ¬ n < datasize(buf, n)
Proof step 6:
m0 + m1 = # buf, m2 +1 ≤ 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 +1) = (datasize(buf, m0 + m2 +1) ≤ m0 ⊃ 0;datasize(buf, m0 + m2 +1) - m0)

Rule argument

indvar: m

Additional information

Used simplifier rules: datasize-base: ⊦ datasize(buf, 0) = 0;%datasize-is-smaller-help: ⊦ ¬ n < datasize(buf, n);%nat freely generated by 0, +1;;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)