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Proof step 10 from proof datasize-at-h (previous step)

n < # buf, datasize(buf, m) < m, m ≤ # buf, n < m, datasize(buf, m) ≤ n, datasize(buf, m) < # buf ⊦ m = 0, buf[n] = empty, # buf = 0

User applied rule structural induction

And obtained the following new goals

Proof step 9:
∀ n, buf. n < # buf ∧ datasize(buf, m0) < m0 ∧ m0 ≤ # buf ∧ n < m0 ∧ datasize(buf, m0) ≤ n ∧ datasize(buf, m0) < # buf → m0 = 0 ∨ buf[n] = empty ∨ # buf = 0, n < # buf, datasize(buf, m0 +1) < m0 +1, m0 +1 ≤ # buf, n < m0 +1, datasize(buf, m0 +1) ≤ n, datasize(buf, m0 +1) < # buf ⊦ m0 +1 = 0, buf[n] = empty, # buf = 0

Rule argument

indvar: m

Additional information

[Concretesimprules((Csimpgen(nat freely generated by 0, +1;)))]