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Proof step 30 from proof inv-get-gc-block (previous step)

# lpt = # avol, # kar = 0, keyset(bin-heap(kar, m)) = gc-heap(lpt, log), bin-heap-inv(bin-heap(kar, m), lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), bufs-log-only(bleb, log, lpt), freelist-cons(lpt, freelist), log-group-block(log, lpt), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log) ⊦ m = 0, dups(log)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size)

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: bin-heap-inv-def seq: ⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) subst: [lpt, bh] → [lpt, bin-heap(kar, m)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ bin-heap(kar, m).size = m; (s)% ⊦ bin-heap(kar, m).ar = kar; (s)% ⊦ ¬ 2exp-size(0); (s) Used terms: lpt, bin-heap(kar, m)