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Proof step 38 from proof refine-add-ind (previous step)

# lpt0 = # avol, # lpt1 = # avol, isbuf0 ↔ pstate = readonly, isbuf2 ↔ pstate = readonly, lpt1[bleb.leb] = mklp(m4, m3, lpf, m2), adr = adr2, adr1 = adr0, buf = mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize), ¬ isbuf0, 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, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), 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), istore0 ⊑ istore, isbuf1 → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf1, pstate ≠ readonly → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_INDEX_NODES ∧ avol[bleb.leb].mapped? ∧ (m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # avol[bleb.leb].data), pstate.index? ∨ pstate = readonly ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, bleb, isbuf2; ; bleb1); encode_index_node#(ind, 0; m1, buf; err); 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 → ⟨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)), dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# lpt1 = # avol, # lpt0 = # avol, lpt1[pstate.lnum] = mklp(istore[pstate.lnum].ref-size, m3, LP_INDEX_NODES, m2), avol[pstate.lnum] = 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, pstate ≠ unbuffered, pstate ≠ readonly, pstate.index?, pstate.lnum < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), pstate.lnum ∈ istore, istore0 ⊑ istore, ¬ dups(log1), m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, isbuf1 → synced(avol) ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, buffered(pstate.lnum), false; ; bleb1); buf := mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize); encode_index_node#(ind, 0; m1, buf; err); adr := adr2; isbuf2 := pstate = readonly; bleb := buffered(pstate.lnum); 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 → ⟨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))

Rule argument

Additional information

Used simplifier rules: fwd-in-istore-lpt: ⊦ n ∈ istore ∧ abs-istore(avol, lpt, istore) → n < # lpt ∧ lpt[n].ref-size = istore[n].ref-size ∧ lpt[n].flags = LP_INDEX_NODES;% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ mapped(buf).data = buf; (s)% ⊦ ¬ unbuffered.index?; (s)% ⊦ unbuffered ≠ readonly; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ buffered(m).leb = m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)