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Proof step 15 from proof inv-set-gblock-refsize (previous step)

# lpt1 = # avol, lpt[m].gcheapidx = lpt[m].gcheapidx, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), bh1 = gch, gch = gch, keyset(gch) = gc-heap(lpt1, log), lpt = lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt = lpt, lpt2 = lpt, m3 = m, n0 = lpt[m].gcheapidx, natkey1 = m0, natkey2 = n, m < # avol, bin-heap-inv(gch, lpt1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), log-group-block(log, lpt1), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), key-index(m0, m) ∈ gc-heap(lpt1, log), key-index(m0, m) ∈ keyset(gch) ⊦ [gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)] ( bin-heap-inv(gch, lpt) ∧ id-idx(lpt2, lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(natkey1, m3)) ++ key-index(natkey2, m3) → lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ bufs-log-only(bleb, log, lpt) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ buf-ro-rw-mode(isbuf, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log)), # gc-heap(lpt1, log) = 0, gc-heap(lpt1, log) = ∅, dups(log), m ∈ log

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), bh1 = gch, keyset(gch) = gc-heap(lpt1, log), lpt = lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], # gc-heap(lpt1, log) ≠ 0, gc-heap(lpt1, log) ≠ ∅, m < # avol, bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), log-group-block(log, lpt1), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), key-index(m0, m) ∈ gc-heap(lpt1, log), ¬ dups(log), ¬ m ∈ log ⊦ [gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)] ( bin-heap-inv(gch, lpt) ∧ id-idx(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(m0, m)) ++ key-index(n, m) → keyset(gch) = gc-heap(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], log) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ m1 ≤ LEB_SIZE ∧ lpt-ram-flash(lpt, lpt0, log))

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).size = n3; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)%⊦ lpt[n] = mklp(m0, n1, lpf0, m1) → ( buf-ro-rw-mode (boolvar, bleb, lpt[n, mklp(n0, n1, lpf1, n2)], avol) ↔ buf-ro-rw-mode(boolvar, bleb, lpt, avol)); (s)%lpt[n].flags = lp.flags ⊦ bufs-log-only(bleb, nx, lpt) → bufs-log-only(bleb, nx, lpt[n, lp]); (s)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ id-idx(lpt0, lpt1) → (lpt-leb-size(lpt1) ↔ lpt-leb-size(lpt0)); (s)%⊦ id-idx(lpt0, lpt1) → ( buf-ro-rw-mode(boolvar, bleb, lpt1, avol) ↔ buf-ro-rw-mode(boolvar, bleb, lpt0, avol)); (s)%⊦ id-idx(lpt0, lpt1) → (bufs-log-only(bleb, nx, lpt1) ↔ bufs-log-only(bleb, nx, lpt0)); (s)% ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)%⊦ id-idx(lpt0, lpt1) → (freelist-cons(lpt1, freelist) ↔ freelist-cons(lpt0, freelist)); (s)% ⊦ id-idx(lpt0, lpt1) → (lpt-free-unref(lpt1) ↔ lpt-free-unref(lpt0)); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)