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Proof step 27 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 26:
∀ buf, n0. subarray(buf, n0, n) = mkempbuf(n) ∧ n0 + n ≤ # buf → datasize(buf, n0 + n) = datasize(buf, n0), subarray(buf, n0, n +1) = mkempbuf(n +1), n0 + n +1 ≤ # buf ⊦ datasize(buf, n0 + n +1) = datasize(buf, n0)

Rule argument

indvar: n1

Additional information

[Concretesimprules((Csimpgen(nat freely generated by 0, +1;) Csimpnamedseq(array-copy,buffer,subarray-zero, ⊦ subarray(buf, n, 0) = mkbuf(0)) 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)))]