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Proof step 4 from proof datasize-ls-samedata (previous step)

# buf0 = # buf1, datasize(buf0, # buf1) < datasize(buf1, # buf1), range=(buf0, 0, buf1, 0, datasize(buf1, # buf1)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # buf0 = # buf1 ∧ m ≤ # buf0 ∧ range=(buf0, 0, buf1, 0, datasize(buf1)) → ¬ datasize(buf0, m) < datasize(buf1, m)
Proof step 6:
⊦ datasize(buf) = datasize(buf, # buf)

Rule argument

spec: <toplevel> name: datasize-ls-samedata-h seq: ⊦ # buf0 = # buf1 ∧ m ≤ # buf0 ∧ range=(buf0, 0, buf1, 0, datasize(buf1)) → ¬ datasize(buf0, m) < datasize(buf1, m) subst: [buf1, m, buf0] → [buf1, # buf1, buf0] flags: <all paths>

Additional information

Used simplifier rules: datasize: ⊦ datasize(buf) = datasize(buf, # buf);% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: buf1, # buf1, buf0