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Proof step 23 from proof inv-read-buf (previous step)

# lpt = # avol, # buf1 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf2, avol[m3] = mapped(buf2), m3 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m5, m4), mapped(buf2), rofs), # buf2 ≤ LEB_SIZE, n ≤ # buf, m0 + n ≤ LEB_SIZE, m5 ≤ m0 + n, m0 ≤ m5 + m4, m5 ≤ LEB_SIZE, ¬ m0 ≤ m5 → m5 ≤ m0 ⊦ (m0 ≤ m5 ⊃ 0;m0 - m5) + min(n - (m0 ≤ m5 ⊃ m5 - m0;0), m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)) ≤ EB_PAGE_SIZE ∧ (m0 ≤ m5 ⊃ m5 - m0;0) + min(n - (m0 ≤ m5 ⊃ m5 - m0;0), m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)) ≤ # buf ∧ (m0 ≤ m5 ⊃ m5 - m0;0) ≤ n ∧ (m0 ≤ m5 ⊃ 0;m0 - m5) ≤ m4

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 24:
# buf1 = EB_PAGE_SIZE, # lpt = # avol, LEB_SIZE = n0 + # buf2, avol[m3] = mapped(buf2), m3 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m5, m4), mapped(buf2), rofs), m5 ≤ LEB_SIZE, m0 ≤ m5 + m4, m5 ≤ m0 + n, m0 + n ≤ LEB_SIZE, n ≤ # buf, # buf2 ≤ LEB_SIZE, (m0 ≤ m5 ⊃ m5 - m0;0) ≤ n, ¬ m0 ≤ m5 → m5 ≤ m0 ⊦ (m0 ≤ m5 ⊃ 0;m0 - m5) + min(n - (m0 ≤ m5 ⊃ m5 - m0;0), m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)) ≤ EB_PAGE_SIZE ∧ (m0 ≤ m5 ⊃ m5 - m0;0) + min(n - (m0 ≤ m5 ⊃ m5 - m0;0), m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)) ≤ # buf ∧ (m0 ≤ m5 ⊃ m5 - m0;0) ≤ n ∧ (m0 ≤ m5 ⊃ 0;m0 - m5) ≤ m4

Rule argument

fma: (m0 ≤ m5 ⊃ m5 - m0;0) ≤ n

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ¬ m < 0; (s)% ⊦ m ≤ n → (n - m = 0 ↔ n = m); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ n ≠ n0 → (n < n0 ↔ ¬ n0 < n); (ss)% ⊦ m < n → ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: (m0 ≤ m5 ⊃ m5 - m0;0) ≤ n