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Proof step 25 from proof inv-write-buf (previous step)

# 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)))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 26:
# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf2), buf = copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), m0 = m3, m1 = buffered(m4).leb, n0 = align↓(m2 + n3, EB_PAGE_SIZE), n1 = 0, buffered(m4).isbuf?, m4 < # avol, ebm-vol-inv(avol), is-aligned(m3, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf2), false), 0 + (align↓(m2 + n3, EB_PAGE_SIZE) - m2) ≤ # buf3, m2 + (align↓(m2 + n3, EB_PAGE_SIZE) - m2) ≤ # copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), 0 + m2 ≤ # buf1, 0 + m2 ≤ # mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), m3 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), m2 ≤ EB_PAGE_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m3 + m2 + n3 ≤ LEB_SIZE, n3 ≤ # buf3, # buf2 ≤ m3, align↓(m2 + n3, EB_PAGE_SIZE) ≥ m2 ⊦ [if m1 < # avol ∧ avol[m1].mapped? ∧ # avol[m1].data ≤ m0 ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m0 + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf then {fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n)) ifnone skip} else abort] ( ebm-vol-inv(avol) ∧ # lpt = # avol → ⟪wbuf := mkwbuf(buf1, m3, 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

pos: right 1

Additional information

Used simplifier rules: apersistence_io_write# (LNUM, OFFSET, N0, N, BUF, PROOTADR, PMAXINO, PLOG, PLPT, PORPHANS ; PVOL ; ERR ) {if LNUM < # PVOL ∧ PVOL[LNUM].mapped? ∧ # PVOL[LNUM].data ≤ OFFSET ∧ is-aligned(OFFSET, EB_PAGE_SIZE) ∧ is-aligned(N, EB_PAGE_SIZE) ∧ OFFSET + N ≤ LEB_SIZE ∧ N0 + N ≤ # BUF then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then if N ≠ 0 then PVOL[LNUM] := mapped ( PVOL[LNUM].data + mkempbuf(OFFSET - # PVOL[LNUM].data) + subarray(BUF, N0, N)) else choose N1 with N1 < N ∧ is-aligned(N1, EB_PAGE_SIZE) in if N1 ≠ 0 then PVOL[LNUM] := mapped ( PVOL[LNUM].data + mkempbuf(OFFSET - # PVOL[LNUM].data) + subarray(BUF, N0, N1)) ifnone skip} else abort };