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Proof step 27 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), keyset(gch) = gc-heap(lpt, nx + n '), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, avol[n].mapped?, ginval < # avol, n < # avol, abs-istore(avol, lpt, istore), abs-nodes(avol[n].data, groupblock(gndx, lax, m).gndlist, groupblock(gndx, lax, m).ladrlist, mklp(m, m0, LP_GROUP_NODES, m1).size = LEB_SIZE), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(n), lpt, avol), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx, lax, m)), log-group-block(nx + n ', lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, nx + n '), n ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), mklp(m, m0, LP_GROUP_NODES, m1).size ≠ LEB_SIZE → mklp(m, m0, LP_GROUP_NODES, m1).size = # avol[n].data ⊦ dups(nx), n ∈ ginval, n ∈ nx, # avol[n].data ≤ LEB_SIZE ∧ avol[n].mapped? ∧ m0 = # avol[n].data ∧ is-aligned(# avol[n].data, 2 * NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# gndx = # lax, # lpt0 = # avol, # lpt = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, avol[n] = mapped(buf), gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), keyset(gch) = gc-heap(lpt, nx + n '), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-istore(avol, lpt, istore), abs-nodes(buf, gndx, lax, m0 = LEB_SIZE), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(n), lpt, avol), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx, lax, m)), log-group-block(nx + n ', lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, nx + n '), n ∈ gstore, # buf ≤ LEB_SIZE, istore0 ⊑ istore, isbuf → synced(avol), m0 ≠ LEB_SIZE → m0 = # buf ⊦ dups(nx), n ∈ ginval, n ∈ nx, is-aligned(# buf, 2 * NODE_HEADER_SIZE) ∧ m0 = # buf

Rule argument

Additional information

Used simplifier rules: ⊦ awbuf-inv(avol, bleb) ∧ n < # avol ∧ avol[n] = mapped(buf) → ¬ LEB_SIZE < # buf; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)