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Proof step 15 from proof refine-add-gnds (previous step)

# lpt = # avol, # lpt0 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), gstore[n] = groupblock(gndx, lax, m), keyset(gch) = gc-heap(lpt, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), 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(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m)), log-group-block(nx + n ', lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, nx + n '), n ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol) ⊦ dups(nx), n ∈ ginval, n ∈ nx, 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

Proof step 16:
⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size))
Proof step 17:
# 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), 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), ∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ dups(nx), n ∈ nx, n ∈ ginval, avol[n].mapped? ∧ (gndx0 ≠ [] ∧ m0 + gndx0.flashsize ≤ LEB_SIZE → m0 = # avol[n].data)

Rule argument

spec: persistence-base name: abs-gstore-def seq: ⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ n. ( n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ ( n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size)) subst: [ginval, gstore, lpt, avol] → [ginval, gstore, lpt, avol] flags: <all paths>

Additional information

Used terms: ginval, gstore, lpt, avol