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Proof step 226 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, # gndx1 = # lax1, (elems nx ∪ dom gstore0) ++ n1 = dom gstore1 ∪ ginval, lpt1[n1] = mklp(m, # buf1, LP_GROUP_NODES, m3), avol[n1] = mapped(buf1), gstore1[n1] = groupblock(gndx1, lax1, m), keyset(gch) = gc-heap(lpt1, nx + n1 '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < gndx0.flashsize, ginval < # avol, n0 < # lax0, n1 < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), abs-nodes(subarray(buf0, 0, n), # buf1, prefixn(n0, gndx0), prefixn(n0, lax0), true), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m)), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , isbuf → synced(avol) ⊦ gndx0 = [], lax0 = [], n = 0, n0 = # lax0, abs-nodes(buf1 + subarray(buf0, 0, n), gndx1 + prefixn(n0, gndx0), lax1 + prefixn(n0, lax0), true), dups(nx), n1 ∈ ginval, n1 ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-list, inst: encoding-group-node name: abs-nodes-append seq: ⊦ abs-nodes(buf0, gndx, lax0, false) → ( abs-nodes(buf0 + buf1, gndx + gndx0, lax0 + lax1, weak) ↔ abs-nodes(buf1, # buf0, gndx0, lax1, weak)) subst: [weak, lax1, lax0, gndx0, gndx, buf1, buf0] → [true, prefixn(n0, lax0), lax1, prefixn(n0, gndx0), gndx1, subarray(buf0, 0, n), buf1] flags: <all paths>

Additional information

Used simplifier rules: abs-nodes-strengthen: ⊦ abs-nodes(buf, gndx, lax, weak) ∧ ¬ abs-nodes(buf, gndx, lax, false) → weak; (forward) from specification abs-list[encoding-group-node]% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE); (ss)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ gndx.flashsize = 0 ↔ gndx = []; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%⊦ abs-nodes(buf, m, gndx, lax0, false) → ( abs-nodes(buf, m, gndx0, lax1, boolvar1) ↔ gndx = gndx0 ∧ lax0 = lax1); (s) Used terms: true, prefixn(n0, lax0), lax1, prefixn(n0, gndx0), gndx1, subarray(buf0, 0, n), buf1