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Proof step 12 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, avol1[m2] = mapped(buf1), adr = adr0, avol = avol0, buf = buf3, buf0 = buf, lpt = lpt0, m = m5, m1 = m2, n0 = 0, ns = ns0, plog = plog0, m2 < # avol1, abs(avol1, bleb, mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), n ≤ # buf3, m0 + n ≤ LEB_SIZE, 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) ⊦ ⟪if m1 < # avol ∧ avol[m1].mapped? ∧ n0 + n ≤ # buf0 ∧ m0 + n ≤ LEB_SIZE then {fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), m0, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf0, 0, buf, 0, n0) ∧ range=(buf0, n0 + n, buf, n0 + n, # buf0 - n0 + n) in buf0 := buf} else abort; buf := buf0; if err = ESUCCESS ∧ buffered(m2) = bleb ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n then let m1 = (m0 ≤ m6 ⊃ 0;m0 - m6), m = (m0 ≤ m6 ⊃ m6 - m0;0) in buf := copy(buf2, m1, buf, m, min(n - m, m4 - m1))⟫ ⟨awbuf_read_buf#(m2, m0, n, adr0, m5, plog0, avol1, lpt0, ns0, bleb, rofs; buf3; err0)⟩ (buf = buf3 ∧ err = err0)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 13:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m2] = mapped(buf1), adr = adr0, avol = avol0, buf = buf3, buf0 = buf, lpt = lpt0, m = m5, m1 = m2, n0 = 0, ns = ns0, plog = plog0, m2 < # avol1, abs(avol1, bleb, mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), m0 + n ≤ LEB_SIZE, n ≤ # buf3, 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) ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), m0, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf0, 0, buf, 0, n0) ∧ range=(buf0, n0 + n, buf, n0 + n, # buf0 - n0 + n) in buf0 := buf; buf := buf0; if err = ESUCCESS ∧ buffered(m2) = bleb ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n then let m1 = (m0 ≤ m6 ⊃ 0;m0 - m6), m = (m0 ≤ m6 ⊃ m6 - m0;0) in buf := copy(buf2, m1, buf, m, min(n - m, m4 - m1))⟫ ⟨awbuf_read_buf#(m2, m0, n, adr0, m5, plog0, avol1, lpt0, ns0, bleb, rofs; buf3; err0)⟩ (buf = buf3 ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # avol ⊦ abs(avol, bleb, wbuf, avol0, rofs) ∧ avol[n] = mapped(buf) → (avol0[n].mapped? ↔ true); (ss)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic