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Proof step 6 from proof refine-add-log-leb (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf0 = EB_PAGE_SIZE, avol1[m5] = mapped(buf), adr = adr0, avol = avol0, bleb0 = bleb, lpt = lpt0, m = m2, m0 = # avol1[m5].data, m1 = m5, ns = ns0, plog = plog0, plog1 = plog0, wbuf = mkwbuf(buf0, m4, m3), avol1[m5].mapped?, m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, rofs), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], rofs) ⊦ ⟪if ¬ rofs → bleb = buffered(m1) ∨ (bleb = nobuffer ∨ wbuf.nbytes = 0) ∧ m1 < # avol ∧ avol[m1].mapped? ∧ m0 = # avol[m1].data then if rofs then err := EROFS else {apersistence_io_add_log_leb#(m1, adr, m, avol, lpt, ns; plog; err); if err = ESUCCESS then wbuf_move_buf#(m1, m0, rofs, avol; bleb, wbuf; err)} else abort⟫ ⟨awbuf_add_log_leb#(m5, # avol1[m5].data, adr0, m2, avol1, lpt0, ns0, rofs; plog1, bleb0; err0)⟩ (abs(avol1, bleb, wbuf, avol0, rofs) ∧ bleb0 = bleb ∧ plog1 = plog ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
# buf0 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m5] = mapped(buf), adr = adr0, avol = avol0, bleb0 = bleb, lpt = lpt0, m = m2, m0 = # avol1[m5].data, m1 = m5, ns = ns0, plog = plog0, plog1 = plog0, wbuf = mkwbuf(buf0, m4, m3), wbuf = mkwbuf(buf1, m6, m7), avol1[m5].mapped?, m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, rofs), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], rofs) ⊦ ⟪if ¬ rofs → bleb = buffered(m1) ∨ (bleb = nobuffer ∨ m7 = 0) ∧ m1 < # avol ∧ avol[m1].mapped? ∧ m0 = # avol[m1].data then if rofs then err := EROFS else {apersistence_io_add_log_leb#(m1, adr, m, avol, lpt, ns; plog; err); if err = ESUCCESS then wbuf_move_buf#(m1, m0, rofs, avol; bleb, wbuf; err)} else abort⟫ ⟨awbuf_add_log_leb#(m5, # avol1[m5].data, adr0, m2, avol1, lpt0, ns0, rofs; plog1, bleb0; err0)⟩ (abs(avol1, bleb, wbuf, avol0, rofs) ∧ bleb0 = bleb ∧ plog1 = plog ∧ err = err0)

Rule argument

spec: wbuf name: elim seq: ⊦ (buf = wbuf.content ∧ m = wbuf.offset) ∧ m0 = wbuf.nbytes ↔ wbuf = mkwbuf(buf, m, m0) subst: [wbuf, buf, m, m0] → [wbuf, buf1, m6, m7]

Additional information

Used simplifier rules: ⊦ (buf = wbuf.content ∧ m = wbuf.offset) ∧ m0 = wbuf.nbytes ↔ wbuf = mkwbuf(buf, m, m0); (elim) Used terms: wbuf, buf1, m6, m7