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Proof step 19 from proof refine-enter-readonly (previous step)

# avol0 = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), n < # avol, m < # avol, awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), rofs), n < # avol → (n ≠ m → avol[n] = avol0[n]) ∧ (¬ rofs ∧ n = m → avol[m] = mapped(buf0 + subarray(buf, 0, m1))) ∧ ( rofs ∧ n = m → m2 = # buf0 ∧ avol[m] = mapped(buf0 + subarray(buf, 0, m1)) ∨ m2 < # buf0 ∧ m2 + m1 < # buf0 ∧ avol[m] = mapped(buf0) ∧ subarray(buf, 0, m1) = subarray(buf0, m2, m1)) ⊦ (n ≠ m → avol[n] = avol0[n]) ∧ ( n = m → m2 = # buf0 ∧ avol[m] = mapped(buf0 + subarray(buf, 0, m1)) ∨ m2 < # buf0 ∧ m2 + m1 < # buf0 ∧ avol[m] = mapped(buf0) ∧ subarray(buf, 0, m1) = subarray(buf0, m2, m1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# avol0 = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol[m] = mapped(buf0 + subarray(buf, 0, m1)), avol0[m] = mapped(buf0), m < # avol, awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), false) ⊦ m2 = # buf0, m2 < # buf0 ∧ m1 = 0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ buf + buf0 = buf ↔ # buf0 = 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic