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Proof step 7 from proof datasize-zero-h (previous step)

(buf[m0] = empty ⊃ datasize(buf, m0);m0 + 1) = 0, n ≤ m0, ∀ buf. datasize(buf, m0) = 0 ↔ (∀ n. n < m0 → buf[n] = empty) ⊦ buf[n] = empty

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
(buf[m0] = empty ⊃ datasize(buf, m0);m0 + 1) = 0, buf[m0] = empty, n ≤ m0, ∀ buf. datasize(buf, m0) = 0 ↔ (∀ n. n < m0 → buf[n] = empty) ⊦ buf[n] = empty

Rule argument

fma: buf[m0] = empty

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: buf[m0] = empty