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Proof step 12 from proof refine-read-ind (previous step)

# lpt0 = # avol, # lpt = # avol, lpt[m0] = mklp(m3, m4, LP_INDEX_NODES, m5), istore[m0] = indexblock(indx, lax, m3), ind = ind0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m0 < # avol, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), 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(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(indexblock(indx, lax, m3)), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ istore, @(m1, m2) ∈ lax, istore0 ⊑ istore, ¬ dups(log1), 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) ⊦ ⟪persistence_read_ind#(@(m0, m1, m2), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ind; err)⟫ ⟨apersistence_read_ind#(@(m0, m1, m2), 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 rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ladr ∈ lax ↔ (∃ lax0, lax1. lax = lax0 + (ladr + lax1))
Proof step 14:
# lpt = # avol, # lpt0 = # avol, istore[m0] = indexblock(indx, lax, m3), lpt[m0] = mklp(m3, m4, LP_INDEX_NODES, m5), 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-istore(avol, lpt, istore), 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(indx, lax, m3)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), 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, 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, ∃ lax0, lax1. lax = lax0 + (@(m1, m2) + lax1) ⊦ ⟪persistence_read_ind#(@(m0, m1, m2), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ind; err)⟫ ⟨apersistence_read_ind#(@(m0, m1, m2), 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)

Rule argument

spec: list, inst: laddress-list name: in-def seq: ⊦ ladr ∈ lax ↔ (∃ lax0, lax1. lax = lax0 + (ladr + lax1)) subst: [lax, ladr] → [lax, @(m1, m2)] flags: <all paths>

Additional information

Used terms: lax, @(m1, m2)