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Proof step 6 from proof refine-add-ind (previous step)

# lpt = # avol, # lpt0 = # avol, lpt[pstate.lnum].flags = LP_INDEX_NODES, lpt[pstate.lnum].ref-size = istore[pstate.lnum].ref-size, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.index?, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), 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), pstate.lnum ∈ istore, istore0 ⊑ istore, isbuf → synced(avol), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore ⊦ pstate = unbuffered, pstate = readonly, dups(log1), avol[pstate.lnum].mapped? ∧ (lpt[pstate.lnum].size + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → lpt[pstate.lnum].size = # avol[pstate.lnum].data)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
# lpt0 = # avol, # lpt = # avol, lpt[m].flags = LP_INDEX_NODES, lpt[m].ref-size = istore[m].ref-size, keyset(gch) = gc-heap(lpt, log1), pstate = index(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.index?, m < # avol, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(m)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(m), lpt, avol), bufs-log-only(buffered(m), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), m ∈ istore, istore0 ⊑ istore, pstate.journal? → log1 ≠ [] ∧ m = log1.last ∧ m ∈ gstore, isbuf → synced(avol) ⊦ pstate = readonly, pstate = unbuffered, dups(log1), avol[m].mapped? ∧ (lpt[m].size + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → lpt[m].size = # avol[m].data)

Rule argument

spec: persistence-state name: elim-02 seq: ⊦ pstate.index? → (m = pstate.lnum ↔ pstate = index(m)) subst: [pstate, m] → [pstate, m]

Additional information

Used simplifier rules: ⊦ pstate.index? → (m = pstate.lnum ↔ pstate = index(m)); (elim) Used terms: pstate, m