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Proof step 43 from proof refine-add-ind (previous step)

# lpt1 = # avol, # lpt0 = # avol, istore[m0] = indexblock(indx, lax, m4), lpt1[m0] = mklp(m4, m3, LP_INDEX_NODES, m2), avol[m0] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m0 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(m0)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m0), lpt1, avol), bufs-log-only(buffered(m0), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(indexblock(indx, lax, m4)), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), m0 ∈ istore, istore0 ⊑ istore, ¬ dups(log1), m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf, isbuf1 → synced(avol) ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, buffered(m0), false; ; bleb1); buf := mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize); encode_index_node#(ind, 0; m1, buf; err); adr := adr2; isbuf2 := false; bleb := buffered(m0); if err = ESUCCESS then if ¬ lpt1[bleb1.leb].size + m1 ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(m1, buf, adr0, m, log1, lpt0, ns0, bleb; avol, isbuf2; err); if err = ESUCCESS then {adr := @(bleb1.leb, lpt1[bleb1.leb].size, m1); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + m1, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx)} else lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟨pstate := index(m0); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m, ns0; adr2, istore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ adr = adr2 ∧ err = err0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 44:
# lpt0 = # avol, # lpt1 = # avol, isbuf ↔ false, avol[m0] = mapped(buf), lpt1[m0] = mklp(m4, m3, LP_INDEX_NODES, m2), istore[m0] = indexblock(indx, lax, m4), adr = adr0, bleb0 = buffered(m0), keyset(gch) = gc-heap(lpt1, log1), log = log1, lpt = lpt0, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m0 < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(m0)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m0), lpt1, avol), bufs-log-only(buffered(m0), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m4)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), m0 ∈ istore, istore0 ⊑ istore, isbuf1 → synced(avol), m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf ⊦ [bleb := bleb0; buf := mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize); encode_index_node#(ind, 0; m1, buf; err); adr := adr2; isbuf2 := false; bleb0 := buffered(m0); if err = ESUCCESS then if ¬ lpt1[bleb.leb].size + m1 ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb0; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(m1, buf, adr0, m, log1, lpt0, ns0, bleb0; avol, isbuf2; err); if err = ESUCCESS then {adr := @(bleb.leb, lpt1[bleb.leb].size, m1); lpt1[bleb.leb] := mklp(lpt1[bleb.leb].ref-size, lpt1[bleb.leb].size + m1, lpt1[bleb.leb].flags, lpt1[bleb.leb].gcheapidx)} else lpt1[bleb.leb] := mklp(lpt1[bleb.leb].ref-size, LEB_SIZE, lpt1[bleb.leb].flags, lpt1[bleb.leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb0; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb0, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb0, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb0) ∧ # lpt0 = # avol → ⟨pstate := index(m0); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m, ns0; adr2, istore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb0 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb0 = buffered(pstate.lnum)) ∧ adr = adr2 ∧ err = err0)), dups(log1)

Rule argument

pos: right 1

Additional information

Used simplifier rules: awbuf_get_buf# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; WBUFLEB0 ) {WBUFLEB0 := WBUFLEB};