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Proof step 19 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf2), m4 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), false), 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 ⊦ ⟪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); 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)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: apersistence-io-asm name: inv-write seq: ebm-vol-inv(avol), # lpt = # avol, m < # avol, avol[m].mapped?, # avol[m].data ≤ m0, is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ ⟪apersistence_io_write# (m, m0, n0, n, buf, adr, m1, plog, lpt, ns; avol; err)⟫ (ebm-vol-inv(avol) ∧ # lpt = # avol) subst: [ns, lpt, plog, m1, adr, buf, n, n0, m0, m, avol, err] → [ns, lpt, plog, m, adr, copy (buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), align↓(m2 + n3, EB_PAGE_SIZE), 0, m1, buffered(m4).leb, avol, err] flags: <all paths>

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