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Proof step 20 from proof refine-add-gnds (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 = ∅, n < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-leb(avol[n], groupblock(gndx, lax, m), mklp(m, m0, LP_GROUP_NODES, m1)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(n), lpt, avol), bufs-log-only(buffered(n), nx + n ', lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx, lax, m)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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) ⊦ dups(nx), n ∈ nx, n ∈ ginval, avol[n].mapped? ∧ (gndx0 ≠ [] ∧ m0 + gndx0.flashsize ≤ LEB_SIZE → m0 = # avol[n].data)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-leb, inst: encoding-group-node name: abs-leb-def seq: ⊦ abs-leb(aleb, gblock, lp) ↔ aleb.mapped? ∧ abs-nodes (aleb.data, gblock.gndlist, gblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data) subst: [lp, gblock, aleb] → [mklp(m, m0, LP_GROUP_NODES, m1), groupblock(gndx, lax, m), avol[n]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ gndx.flashsize = 0 ↔ gndx = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: mklp(m, m0, LP_GROUP_NODES, m1), groupblock(gndx, lax, m), avol[n]