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Proof step 2 from proof datasize-split-empty (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ datasize(buf) = datasize(buf, # buf)
Proof step 4:
buf1 = mkempbuf(# buf1) ⊦ datasize(buf0 + buf1, # buf0 + # buf1) = datasize(buf0, # buf0)

Rule argument

Additional information

Used simplifier rules: datasize: ⊦ datasize(buf) = datasize(buf, # buf);%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)