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Proof step 46 from proof refine-read-gnd (previous step)

# gndx0 = # lax1, # buf1 = 2 * NODE_HEADER_SIZE + gnd2.alignedsize, # gndx1 = # lax0, # lpt = # avol, # lpt0 = # avol, lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore2[m0] = groupblock(gndx0 + gnd2 ' + gndx1, lax1 + @(# buf0, # buf1) ' + lax0, m3), avol[m0] = mapped(buf0 + buf1 + buf2), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, m0 < # avol, abs-istore(avol, lpt, istore2), abs-node(buf1, gnd2), abs-nodes(buf0 + buf1 + buf2, gndx0 + gnd2 ' + gndx1, 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, istore1, gstore1), freelist-cons(lpt, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(groupblock(gndx0 + gnd2 ' + gndx1, 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 ∈ gstore2, istore1 ⊑ istore2, err1 = ESUCCESS → gnd2 = gnd1, m4 ≠ LEB_SIZE → m4 = # buf0 + # buf1 + # buf2, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → isbuf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ dups(log1), m0 ∈ ginval, @(m0, # buf0, # buf1) ∈ gstore2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ablock-store-inv, inst: group-store name: in seq: ⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist subst: [gstore, adr] → [gstore2, @(m0, # buf0, # buf1)] 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)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ ladr ∈ lax + lax0 ↔ ladr ∈ lax ∨ ladr ∈ lax0; (s)% ⊦ ladr ∈ ladr0 ' + lax ↔ ladr = ladr0 ∨ ladr ∈ lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list] Used terms: gstore2, @(m0, # buf0, # buf1)