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Proof step 5 from proof refine-add-gnds (previous step)

# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, ax = ax0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, 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), 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), istore0 ⊑ istore, 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), pstate.journal? ∨ pstate = readonly ⊦ dups(log1), lpt-free-unref(lpt) ∧ lpt-free-unref(lpt0) ∧ freelist-cons(lpt, freelist) ∧ log1 = log1 ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ ¬ dups(log1) ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-leb-size(lpt0) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ LEB_SIZE = LEB_SIZE ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol ∧ ( ¬ isbuf0 → bleb.isbuf? ∧ bleb.leb < # lpt ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∧ bleb.leb ∈ log1 ∧ avol[bleb.leb].mapped? ∧ (gndx0 ≠ [] ∧ lpt[bleb.leb].size + gndx0.flashsize ≤ LEB_SIZE → lpt[bleb.leb].size = # avol[bleb.leb].data))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# 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)

Rule argument

Additional information

Used simplifier rules: fwd-in-gstore-lpt: ⊦ n ∈ gstore ∧ abs-gstore(avol, lpt, gstore, ginval) → n < # lpt ∧ lpt[n].ref-size = gstore[n].ref-size ∧ lpt[n].flags = LP_GROUP_NODES;%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ nx.last ∈ nx ↔ nx ≠ []; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ¬ unbuffered.journal?; (s)% ⊦ unbuffered ≠ readonly; (s)%fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]