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Proof step 23 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, (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(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt0, log)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-base name: lpt-ram-flash-write-same seq: n < # lpt ⊦ lpt[n] = mklp(n0, m, lpf, n2) → ( lpt-ram-flash(lpt[n, mklp(m0, m, lpf, m2)], lpt0, nx) ↔ lpt-ram-flash(lpt, lpt0, nx)) subst: [n0, n2, nx, lpt0, m2, lpf, m, m0, n, lpt] → [m0, m2, log, lpt0, m2, LP_GROUP_NODES, m1, n, m, lpt1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: m0, m2, log, lpt0, m2, LP_GROUP_NODES, m1, n, m, lpt1