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Proof step 2 from proof datasize-append-lower-h (previous step)

m ≤ # buf0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, m)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ datasize(buf, 0) = 0
Proof step 4:
m0 +1 ≤ # buf0, ∀ buf0, buf1. m0 ≤ # buf0 → datasize(buf0 + buf1, m0) = datasize(buf0, m0) ⊦ datasize(buf0 + buf1, m0 +1) = datasize(buf0, m0 +1)

Rule argument

term: m

Additional information

Used simplifier rules: datasize-base: ⊦ datasize(buf, 0) = 0;%nat freely generated by 0, +1;;