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Proof step 23 from proof refine-unmap (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m] = mapped(buf0), n < # avol1, m4 < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs) ⊦ m4 = m, (n ≠ m → avol1[m4, unmapped][n] = avol0[m4, unmapped][n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m3 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m3 < # buf0 ∧ m3 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m3, m2))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 24:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m < # avol1, m4 < # avol1, n < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs) ⊦ m4 = m, n = m4, (n ≠ m → avol1[m4, unmapped][n] = avol0[m4, unmapped][n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m3 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m3 < # buf0 ∧ m3 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m3, m2))

Rule argument

fma: n = m4

Additional information

Used simplifier rules: ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # avol ⊦ avol[m, aleb][m] = aleb; (s) Used formulas: n = m4