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Proof step 5 from proof refine-add-log-leb (previous step)

# buf0 = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, avol[m] = mapped(buf), bleb0 = bleb, plog = plog0, wbuf = mkwbuf(buf0, m0, m1), m < # avol, abs(avol, bleb, mkwbuf(buf0, m0, m1), avol0, rofs), awbuf-inv(avol, bleb), ebm-vol-inv(avol0), synced(avol), bleb ≠ nobuffer → bleb.leb < # avol ∧ wbuf-cons(mkwbuf(buf0, m0, m1), avol0[bleb.leb], rofs) ⊦ ⟪wbuf_add_log_leb#(m, # avol[m].data, rofs, adr0, m2, avol0, lpt0, ns0; bleb, wbuf, plog0; err)⟫ ⟨awbuf_add_log_leb#(m, # avol[m].data, adr0, m2, avol, lpt0, ns0, rofs; plog, bleb0; err0)⟩ (abs(avol, bleb, wbuf, avol0, rofs) ∧ bleb0 = bleb ∧ plog = plog0 ∧ err = err0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 6:
# 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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: wbuf_add_log_leb# (LNUM, OFFSET, ROFS, PROOTADR, PMAXINO, PVOL, PLPT, PORPHANS ; BUFLEB, WBUF, PLOG ; ERR ) {if ¬ ROFS → BUFLEB = buffered(LNUM) ∨ (BUFLEB = nobuffer ∨ WBUF.nbytes = 0) ∧ LNUM < # PVOL ∧ PVOL[LNUM].mapped? ∧ OFFSET = # PVOL[LNUM].data then if ROFS then ERR := EROFS else {apersistence_io_add_log_leb# (LNUM, PROOTADR, PMAXINO, PVOL, PLPT, PORPHANS; PLOG; ERR); if ERR = ESUCCESS then wbuf_move_buf# (LNUM, OFFSET, ROFS, PVOL; BUFLEB, WBUF; ERR)} else abort };% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ unmapped ≠ mapped(buf); (s)