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Proof step 126 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, rofs ↔ false, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, buf = buf3, err = err1, m = buffered(m4).leb, buffered(m4).isbuf?, n2 < n0 + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ (∀ n. (n ≠ 0 → n < n3 → avol1[m].mapped? ∧ m < # avol1) ∧ ¬(n ≠ 0 ∧ n < n3 ∧ is-aligned(# avol1[m].data + n, EB_PAGE_SIZE))) ∧ ⟨skip; rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ rofs ∧ err1 = err), ∃ n. (n ≠ 0 → n < n3 → avol1[m].mapped? ∧ m < # avol1) ∧ (n ≠ 0 ∧ n < n3 ∧ is-aligned(# avol1[m].data + n, EB_PAGE_SIZE)) ∧ ⟨avol1[m] := mapped(avol1[m].data + subarray(buf, 0, n)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ rofs ∧ err1 = err), n2 = 0, n3 = 0, abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ true ∧ err1 = err

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 127:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n2 ≠ 0, n3 ≠ 0, n2 < n0 + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, ⌊err1⌋ , ¬ abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ⊦ ∃ n1. n1 ≠ 0 ∧ n1 < n3 ∧ is-aligned(# avol1[m4].data + n1, EB_PAGE_SIZE) ∧ ⟨avol1[buffered(m4).leb] := mapped(avol1[buffered(m4).leb].data + subarray(buf3, 0, n1)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ rofs)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n < # avol ⊦ abs(avol, bleb, wbuf, avol0, rofs) ∧ avol0[n] = mapped(buf) → (avol[n].mapped? ↔ true); (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m).isbuf?; (s)