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

# lpt = # avol, # lpt0 = # avol, lpt[log1.last].flags = LP_GROUP_NODES, pstate.lnum = log1.last, lpt[log1.last].ref-size = gstore[log1.last].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.journal?, ginval < # avol, log1.last < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(log1.last), lpt, avol), bufs-log-only(buffered(log1.last), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(gstore[log1.last]), 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), log1.last ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate.index? → log1.last ∈ istore ⊦ log1 = [], pstate = unbuffered, pstate = readonly, dups(log1), avol[log1.last].mapped? ∧ (gndx0 ≠ [] ∧ lpt[log1.last].size + gndx0.flashsize ≤ LEB_SIZE → lpt[log1.last].size = # avol[log1.last].data)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
# lpt0 = # avol, # lpt = # avol, lpt[log1.last].flags = LP_GROUP_NODES, lpt[log1.last].ref-size = gstore[log1.last].ref-size, keyset(gch) = gc-heap(lpt, log1), m = log1.last, pstate = journal(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.journal?, log1.last < # avol, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(log1.last), lpt, avol), bufs-log-only(buffered(log1.last), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore[log1.last]), 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), log1.last ∈ gstore, istore0 ⊑ istore, pstate.index? → log1.last ∈ istore, isbuf → synced(avol) ⊦ log1 = [], pstate = readonly, pstate = unbuffered, dups(log1), avol[log1.last].mapped? ∧ (gndx0 ≠ [] ∧ lpt[log1.last].size + gndx0.flashsize ≤ LEB_SIZE → lpt[log1.last].size = # avol[log1.last].data)

Rule argument

spec: persistence-state name: elim-01 seq: ⊦ pstate.journal? → (m = pstate.lnum ↔ pstate = journal(m)) subst: [pstate, m] → [pstate, m]

Additional information

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