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Proof step 20 from proof datsize-write-higher-h (previous step)

buf0[n1] = empty, n1 + m < # buf, datasize(buf, # buf) < m + n, datasize(buf, # buf) < # buf, m < # buf, n1 < n, n1 < # buf0, datasize(buf, # buf) ≤ n1 + m, n ≤ # buf0, m + n ≤ # buf, datasize(buf, # buf) ≤ m, ∀ buf1, buf2, m0, n0. ¬ datasize(copy(buf1, 0, buf2, m0, n0), n1 + m) < datasize(buf2, n1 + m) ∨ ¬ datasize(buf2, # buf2) ≤ m0 ∨ ¬ m0 + n0 ≤ # buf2 ∨ ¬ n0 ≤ # buf1 ∨ ¬ n1 + m ≤ # buf2 ⊦ buf[n1 + m] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ datasize(buf) ≤ n ∧ n < # buf → buf[n] = empty
Proof step 22:
⊦ datasize(buf) = datasize(buf, # buf)

Rule argument

spec: <toplevel> name: datasize-at seq: ⊦ datasize(buf) ≤ n ∧ n < # buf → buf[n] = empty subst: [n, buf] → [n1 + m, buf] flags: <all paths>

Additional information

Used simplifier rules: datasize: ⊦ datasize(buf) = datasize(buf, # buf); Used terms: n1 + m, buf