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Proof step 13 from proof datasize-ls-samedata-h (previous step)

# buf0 = # buf1, buf0[m0] = empty, m0 < # buf1, range=(buf0, 0, buf1, 0, datasize(buf1, # buf1)), ∀ buf, buf2. # buf ≠ # buf2 ∨ ¬ datasize(buf, m0) < datasize(buf2, m0) ∨ ¬ range=(buf, 0, buf2, 0, datasize(buf2, # buf2)) ∨ ¬ m0 ≤ # buf2 ⊦ buf1[m0] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ datasize(buf) ≤ n ∧ n < # buf → buf[n] = empty
Proof step 15:
# buf0 = # buf1, buf0[m0] = empty, m0 < # buf1, range=(buf0, 0, buf1, 0, datasize(buf1, # buf1)), ∀ buf, buf2. # buf ≠ # buf2 ∨ ¬ datasize(buf, m0) < datasize(buf2, m0) ∨ ¬ range=(buf, 0, buf2, 0, datasize(buf2, # buf2)) ∨ ¬ m0 ≤ # buf2 ⊦ buf1[m0] = empty, datasize(buf1) ≤ m0 ∧ m0 < # buf1

Rule argument

spec: <toplevel> name: datasize-at seq: ⊦ datasize(buf) ≤ n ∧ n < # buf → buf[n] = empty subst: [n, buf] → [m0, buf1] flags: <all paths>

Additional information

Used terms: m0, buf1