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Proof step 6 from proof datasize-append-h-new (previous step)

# buf0 < m, m ≤ # buf0 + # buf1 ⊦ # buf1 = 0, datasize(buf0 + buf1, m) = (datasize(buf1, m - # buf0) = 0 ⊃ datasize(buf0, # buf0);# buf0 + datasize(buf1, m - # buf0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
m = n0 + # buf0, # buf0 < m, m ≤ # buf0 + # buf1, # buf0 ≤ m ⊦ # buf1 = 0, datasize(buf0 + buf1, m) = (datasize(buf1, n0) = 0 ⊃ datasize(buf0, # buf0);# buf0 + datasize(buf1, n0))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m, # buf0, n]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m, # buf0, n