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Proof step 26 from proof refine-read-ind (previous step)

# indx1 = # lax0, # lpt = # avol, # lpt0 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind1.alignedsize, # indx0 = # lax1, istore[m0] = indexblock(indx0 + ind1 ' + indx1, lax1 + @(# buf0, # buf1) ' + lax0, m3), lpt[m0] = mklp(m3, m4, LP_INDEX_NODES, m5), avol[m0] = mapped(buf0 + buf1 + buf2), ind = ind0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m0 < # 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(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(indexblock(indx0 + ind1 ' + indx1, lax1 + @(# buf0, # buf1) ' + lax0, m3)), 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, istore0 ⊑ istore, ¬ dups(log1), isbuf → 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 → isbuf, m4 ≠ LEB_SIZE → m4 = # buf0 + # buf1 + # buf2 ⊦ ⟪persistence_read_ind#(@(m0, # buf0, # buf1), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ind; err)⟫ ⟨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)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: persistence-asm name: inv-read-ind seq: lpt-free-unref(lpt), log = log0, bufs-log-only(bleb, log, lpt0), # lpt0 = # avol, buf-ro-rw-mode(isbuf, bleb, lpt0, avol), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log), awbuf-inv(avol, bleb), # lpt = # avol, adr.lnum < # avol, avol[adr.lnum].mapped?, adr.pos + adr.size ≤ # avol[adr.lnum].data, ∃ ind. abs-node(subarray(avol[adr.lnum].data, adr.pos, adr.size), ind) ⊦ ⟪persistence_read_ind# (adr, adr0, m, log0, avol, lpt, ns, bleb, isbuf; ind0; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → abs-node (subarray(avol[adr.lnum].data, adr.pos, adr.size), ind0))) subst: [isbuf, bleb, ns, lpt, avol, log0, m, adr0, adr, ind0, err, lpt0, log] → [pstate = readonly, bleb, ns0, lpt0, avol, log1, m, adr1, @(m0, # buf0, # buf1), ind, err, lpt, log1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ @(m, m0, m1).lnum = m; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ abs-node(buf, ind) → (abs-node(buf, ind0) ↔ ind = ind0); (s)