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Proof step 24 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf2), adr0 = adr, buf0 = copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), lpt0 = lpt, m3 = buffered(m4).leb, m5 = m1, m6 = m, n1 = align↓(m2 + n3, EB_PAGE_SIZE), n2 = 0, ns0 = ns, plog0 = plog, avol[buffered(m4).leb].mapped?, m4 < # avol, buffered(m4).leb < # avol, ebm-vol-inv(avol), is-aligned(m1, EB_PAGE_SIZE), is-aligned(align↓(m2 + n3, EB_PAGE_SIZE), EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), false), EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), m2 ≤ EB_PAGE_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m1 + m2 + n3 ≤ LEB_SIZE, n3 ≤ # buf3, # avol[buffered(m4).leb].data ≤ m1, m1 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, 0 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ # copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2) ⊦ [apersistence_io_write# (buffered(m4).leb, m1, 0, align↓(m2 + n3, EB_PAGE_SIZE), copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), adr, m, plog, lpt, ns ; avol ; err)] ( ebm-vol-inv(avol) ∧ # lpt0 = # avol → ⟪wbuf := mkwbuf(buf1, m1, m2); rofs := false; if err = ESUCCESS then {wbuf.content := copy(buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE); wbuf.offset := wbuf.offset + align↓(m2 + n3, EB_PAGE_SIZE); wbuf.nbytes := (m2 + n3) % EB_PAGE_SIZE} else rofs := true⟫ (# wbuf.content = EB_PAGE_SIZE ∧ m4 < # avol ∧ wbuf-cons(wbuf, avol[m4], rofs) ∧ ebm-vol-inv(avol) ∧ # lpt = # avol))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# lpt = # avol, # buf1 = EB_PAGE_SIZE, avol[m4] = mapped(buf2), m4 < # avol, ebm-vol-inv(avol), is-aligned(m1, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), false), # buf2 ≤ m1, n3 ≤ # buf3, m1 + m2 + n3 ≤ LEB_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m2 ≤ EB_PAGE_SIZE, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), EB_PAGE_SIZE ≤ m2 + n3, m1 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ [apersistence_io_write# (buffered(m4).leb, m1, 0, align↓(m2 + n3, EB_PAGE_SIZE), copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), adr, m, plog, lpt, ns ; avol ; err)] ( ebm-vol-inv(avol) ∧ # lpt = # avol → ⟪wbuf := mkwbuf(buf1, m1, m2); rofs := false; if err = ESUCCESS then {wbuf.content := copy(buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE); wbuf.offset := wbuf.offset + align↓(m2 + n3, EB_PAGE_SIZE); wbuf.nbytes := (m2 + n3) % EB_PAGE_SIZE} else rofs := true⟫ (# wbuf.content = EB_PAGE_SIZE ∧ m4 < # avol ∧ wbuf-cons(wbuf, avol[m4], rofs)))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%m ≠ 0 ⊦ is-aligned(align↓(n, m), m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ # 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)