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Proof step 80 from proof refine-commit (previous step)

# lpt2 = # avol1, # avol0 = # avol1, # lpt1 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), n < # avol1, m < # avol1, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), rofs), ⌊err1⌋ , n < # avol1 → (n ≠ m → avol1[n] = avol0[n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m1 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m1 < # buf0 ∧ m1 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m1, m2)) ⊦ (n ≠ m → avol1[n] = avol0[n]) ∧ ( n = m → m1 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m1 < # buf0 ∧ m1 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m1, m2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
# lpt2 = # avol1, # avol0 = # avol1, # lpt1 = # avol1, # buf = EB_PAGE_SIZE, avol1[m] = mapped(buf0 + subarray(buf, 0, m2)), avol0[m] = mapped(buf0), m < # avol1, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), false), ⌊err1⌋ ⊦ m1 = # buf0, m1 < # buf0 ∧ m2 = 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