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Proof step 28 from proof refine-read-ind (previous step)

# indx0 = # lax1, # buf1 = 2 * NODE_HEADER_SIZE + ind1.alignedsize, # indx1 = # lax0, # lpt = # avol, # lpt0 = # avol, isbuf0 ↔ pstate = readonly, avol[m0] = mapped(buf0 + buf1 + buf2), lpt[m0] = mklp(m3, m4, LP_INDEX_NODES, m5), istore[m0] = indexblock(indx0 + ind1 ' + indx1, lax1 + @(# buf0, # buf1) ' + lax0, m3), adr2 = @(m0, # buf0, # buf1), adr3 = adr1, avol0 = avol, bleb0 = bleb, ind = ind0, keyset(gch) = gc-heap(lpt, log1), log1 = log1, log2 = log1, log3 = log1, lpt1 = lpt0, lpt2 = lpt, m1 = m, ns1 = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, avol[@(m0, # buf0, # buf1).lnum].mapped?, m0 < # avol, ginval < # avol, @(m0, # buf0, # buf1).lnum < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-node(buf1, ind1), abs-nodes(buf0 + buf1 + buf2, indx0 + ind1 ' + indx1, lax1 + @(# buf0, # buf1) ' + lax0, m4 = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(indexblock(indx0 + ind1 ' + indx1, lax1 + @(# buf0, # buf1) ' + lax0, m3)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ istore, @(m0, # buf0, # buf1).pos + @(m0, # buf0, # buf1).size ≤ # avol[@(m0, # buf0, # buf1).lnum].data, istore0 ⊑ istore, m4 ≠ LEB_SIZE → m4 = # buf0 + # buf1 + # buf2, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol), ∃ ind. abs-node(subarray(avol[@(m0, # buf0, # buf1).lnum].data, @(m0, # buf0, # buf1).pos, @(m0, # buf0, # buf1).size), ind) ⊦ [persistence_read_ind#(@(m0, # buf0, # buf1), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ind; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → abs-node(subarray(avol0[adr2.lnum].data, adr2.pos, adr2.size), ind)) → ⟨apersistence_read_ind# (@(m0, # buf0, # buf1), adr1, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; ind0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ind = ind0 ∧ err = err0)), dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%a: ⊦ (indx + indx0) + indx1 = indx + indx0 + indx1; from specification list[index-store]% ⊦ m +1 = m + 1; (s)% ⊦ #(ind ' + indx) = (# indx)+1; (s)% ⊦ #(indx + indx0) = # indx + # indx0; (s)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, indx, lax, weak) → # indx = # lax; (forward) from specification abs-list[encoding-index-node]%fwd-inv-iblock: ⊦ inv(istore) ∧ n ∈ istore ∧ istore[n] = iblock → inv(iblock); (forward) from specification apersistence-base% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ abs-node(buf, ind) → (abs-node(buf, ind0) ↔ ind = ind0); (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).lnum = m; (s)