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Proof step 24 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m2] = mapped(buf1), buf = copy(avol0[m2].data + mkempbuf(LEB_SIZE - # avol0[m2].data), m0, buf0, 0, n), buf0 = buf3, buffered(m2) = bleb, err = err0, err = ESUCCESS, m = (m0 ≤ m6 ⊃ m6 - m0;0), m1 = (m0 ≤ m6 ⊃ 0;m0 - m6), avol0[m2].mapped?, m2 < # avol0, m2 < # avol1, abs(avol1, bleb, mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), m1 + min(n - m, m4 - m1) ≤ # buf2, m + min(n - m, m4 - m1) ≤ # buf, m0 ≤ m6 + m4, m6 ≤ m0 + n, 0 + n ≤ # buf0, m0 + n ≤ #(avol0[m2].data + mkempbuf(LEB_SIZE - # avol0[m2].data)), m0 + n ≤ LEB_SIZE, n ≤ # buf3, n ≥ m, m4 ≥ m1, LEB_SIZE ≥ # avol0[m2].data, bleb ≠ nobuffer → bleb.leb < # avol1 ∧ avol0[bleb.leb].mapped? ∧ m4 < EB_PAGE_SIZE ∧ (¬ rofs → # avol0[bleb.leb].data = m6) ∧ (rofs → m6 ≤ # avol0[bleb.leb].data) ∧ is-aligned(m6, EB_PAGE_SIZE), (m0 ≤ m6 ⊃ true;m0 ≥ m6), (m0 ≤ m6 ⊃ m6 ≥ m0;true), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨awbuf_read_buf#(m2, m0, n, adr0, m5, plog0, avol1, lpt0, ns0, bleb, rofs; buf3; err1)⟩ (copy(buf2, m1, buf, m, min(n - m, m4 - m1)) = buf3 ∧ err = err1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf0), buf = copy(buf0 + mkempbuf(LEB_SIZE - # buf0), m0, buf3, 0, n), (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, m4 < EB_PAGE_SIZE, abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m6 ≤ # buf0 + (LEB_SIZE - # buf0), # buf0 ≤ LEB_SIZE, (m0 ≤ m6 ⊃ 0;m0 - m6) ≤ m4, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ n, m0 + n ≤ LEB_SIZE, m0 + n ≤ # buf0 + (LEB_SIZE - # buf0), n ≤ # buf3, m6 ≤ m0 + n, m0 ≤ m6 + m4, (m0 ≤ m6 ⊃ m6 - m0;0) + min(n - (m0 ≤ m6 ⊃ m6 - m0;0), m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ # buf3, (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n - (m0 ≤ m6 ⊃ m6 - m0;0), m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ EB_PAGE_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ LEB_SIZE, ¬ rofs → # buf0 = m6, rofs → m6 ≤ # buf0, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ ⟨awbuf_read_buf#(m2, m0, n, adr0, m5, plog0, avol1, lpt0, ns0, buffered(m2), rofs; buf3; err1)⟩ ( copy(buf2, (m0 ≤ m6 ⊃ 0;m0 - m6), buf, (m0 ≤ m6 ⊃ m6 - m0;0), min(n - (m0 ≤ m6 ⊃ m6 - m0;0), m4 - (m0 ≤ m6 ⊃ 0;m0 - m6))) = buf3 ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ buffered(m).leb = m; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)