[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 25 from proof inv-get-gc-block (previous step)

# lpt = # avol, kar[0] = key-index(natkey, m3), lpt[m3] = mklp(m0, m1, lpf, m2), 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) ⊦ # kar = 0, m = 0, dups(log), key-index(natkey, m3) ∈ keyset(bin-heap(kar, m)), m3 < # avol ∧ ¬ m3 ∈ log ∧ m0 = natkey ∧ lpf = LP_GROUP_NODES, m3 < # avol ∧ lpf = LP_GROUP_NODES ∧ ¬ m3 ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ bin-heap-inv(bh, lpt) → (ki ∈ keyset(bh) ↔ (∃ m. m < bh.size ∧ ki = bh.ar[m]))
Proof step 27:
# lpt = # avol, lpt[m3] = mklp(m0, m1, lpf, m2), kar[0] = key-index(natkey, m3), 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) ⊦ # kar = 0, m = 0, dups(log), ∃ m0. m0 < bin-heap(kar, m).size ∧ key-index(natkey, m3) = bin-heap(kar, m).ar[m0], m3 < # avol ∧ lpf = LP_GROUP_NODES ∧ ¬ m3 ∈ log, m3 < # avol ∧ ¬ m3 ∈ log ∧ m0 = natkey ∧ lpf = LP_GROUP_NODES

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: key-set-in seq: ⊦ bin-heap-inv(bh, lpt) → (ki ∈ keyset(bh) ↔ (∃ m. m < bh.size ∧ ki = bh.ar[m])) subst: [lpt, bh, ki] → [lpt, bin-heap(kar, m), key-index(natkey, m3)] flags: <all paths>

Additional information

Used terms: lpt, bin-heap(kar, m), key-index(natkey, m3)