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Proof step 155 from proof refine-add-gnds (previous step)

# gndx1 = # lax1, # lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), gstore[n] = groupblock(gndx1, lax1, m1), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-istore(avol, lpt1, istore2), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), dups(lax1 + lax0), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx1, lax1, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ gndx0 = [], abs-nodes(buf1 + buf0, gndx1 + gndx0, lax1 + lax0, false), dups(nx), n ∈ ginval, n ∈ 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] → [false, lax0, lax1, gndx0, gndx1, buf0, 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]% ⊦ 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: false, lax0, lax1, gndx0, gndx1, buf0, buf1