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Proof step 26 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), 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, # lpt2 = # avol ∧ m1 ≤ LEB_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt2, lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # lpt[n, lp] = # lpt; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ lpt-leb-size(lpt) → ¬ LEB_SIZE < n1; (s) Used terms: lpt2, lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)]