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Proof step 5 from proof datasize-ls-h (previous step)

m0 ≤ # buf ⊦ m = 0, datasize(buf, m0) < m ↔ ¬(∃ n. m ≤ n + 1 ∧ n < m0 ∧ buf[n] ≠ empty)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ m0 ≤ # buf ∧ m ≠ 0 → (m ≤ datasize(buf, m0) ↔ (∃ n. n + 1 ≥ m ∧ n < m0 ∧ buf[n] ≠ empty))

Rule argument

spec: inst: name: datasize-le-h seq: ⊦ m0 ≤ # buf ∧ m ≠ 0 → ( m ≤ datasize(buf, m0) ↔ (∃ n. n + 1 ≥ m ∧ n < m0 ∧ buf[n] ≠ empty)) subst: [m0, buf, m] → [m0, buf, m] flags: current, []

Additional information

[Concretesimprules(()), Extraterms((m0bufm))]