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Proof step 32 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 1:
⊦ datasize(buf, 0) = 0

Rule argument

indvar: m

Additional information

[Concretesimprules((Csimpnamedseq(datasize-base,,, ⊦ datasize(buf, 0) = 0) Csimpnamedseq(datasize-is-smaller-help,,, ⊦ ¬ n < datasize(buf, n)) Csimpgen(nat freely generated by 0, +1;) Csimpnamedseq(nat-basic2,,add-base, ⊦ n + 0 = n) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat,,lez, ⊦ 0 ≤ m) Csimpnamedseq(nat,,lels-01, ⊦ ¬ m ≤ n ↔ n < m)))]