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Proof step 305 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx, lax, m0), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[n] = mapped(buf), adr = adr0, bleb = buffered((nx + n ').last), keyset(gch) = gc-heap(lpt1, nx + n '), log = nx + n ', lpt = lpt0, ns = ns0, pstate = journal((nx + n ').last), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), buf-ro-rw-mode(true, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx, lax, m0)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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, istore0 ⊑ istore, ⌊err⌋ , isbuf1 → synced(avol), m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, nx + n ', m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ true) ∧ (pstate ≠ readonly → n = pstate.lnum) ∧ ax = ax0 ∧ err = err0), nx + n ' = [], gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 306:
# lpt1 = # avol, # lpt0 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx, lax, m0), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[n] = mapped(buf), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, gndx0 ≠ [], ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx, lax, m0)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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, istore0 ⊑ istore, ⌊err⌋ , ¬ dups(nx), ¬ n ∈ nx, ¬ n ∈ ginval, isbuf1 → synced(avol), m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, nx + n ', m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ (abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate = readonly ∧ ax = ax0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ unbuffered ≠ readonly; (s)%⊦ buf-ro-rw-mode(boolvar, bleb, lpt, avol) → buf-ro-rw-mode(true, bleb, lpt, avol); (s)% ⊦ nx + n ' ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ (nx + n ').last = n; (s)