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Proof step 20 from proof inv-set-gblock-refsize (previous step)

# lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, log), keyset(gch0) = (gc-heap(lpt1, log) -- key-index(m0, m)) ++ key-index(n, m), m < # avol, bin-heap-inv(gch, lpt1), bin-heap-inv(gch0, lpt2), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt2), log-group-block(log, lpt1), log-group-block(log, lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)]), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), key-index(m0, m) ∈ gc-heap(lpt1, log) ⊦ # gc-heap(lpt1, log) = 0, gc-heap(lpt1, log) = ∅, dups(log), m ∈ log, (gc-heap(lpt1, log) -- key-index(m0, m)) ++ key-index(n, m) = gc-heap(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], log) ∧ # lpt2 = # avol ∧ true ∧ m1 ≤ LEB_SIZE ∧ lpt-ram-flash(lpt2, lpt0, log)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch0) = (gc-heap(lpt1, log) -- key-index(m0, m)) ++ key-index(n, m), keyset(gch) = gc-heap(lpt1, log), m < # avol, bin-heap-inv(gch0, lpt2), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt2), 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) ⊦ # gc-heap(lpt1, log) = 0, gc-heap(lpt1, log) = ∅, dups(log), m ∈ log, (gc-heap(lpt1, log) -- key-index(m0, m)) ++ key-index(n, m) = gc-heap(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], log) ∧ # lpt2 = # avol ∧ m1 ≤ LEB_SIZE ∧ lpt-ram-flash(lpt2, lpt0, log)

Rule argument

Additional information

Used simplifier rules: n < # lpt ⊦ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)]); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)