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Proof step 8 from proof bin-heap-inv-write-other (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), n < # lpt ⊦ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt[n, mklp(n0, n1, lpf1, n2)], m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m) ↔ bin-heap-inv(bin-heap(kar, m), lpt), lpf0 = LP_GROUP_NODES

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 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)
Proof step 10:
lpt[n] = mklp(m0, m1, lpf0, m2), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), n < # lpt ⊦ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt[n, mklp(n0, n1, lpf1, n2)], m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m) ↔ bin-heap(kar, m).size ≤ # bin-heap(kar, m).ar ∧ no-dups-idx(bin-heap(kar, m).ar, bin-heap(kar, m).size) ∧ valid-idx(bin-heap(kar, m).ar, lpt, bin-heap(kar, m).size) ∧ 2exp-size(# bin-heap(kar, m).ar) ∧ heap-order(bin-heap(kar, m).ar, bin-heap(kar, m).size), lpf0 = LP_GROUP_NODES

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 terms: lpt, bin-heap(kar, m)