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Proof step 3 from proof bin-heap-inv-write-other-fields (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), n < # lpt ⊦ bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 5:
lpt[n] = mklp(m0, m1, lpf0, m2), n < # lpt ⊦ gch.size ≤ # gch.ar ∧ no-dups-idx(gch.ar, gch.size) ∧ valid-idx(gch.ar, lpt[n, mklp(n0, n1, lpf1, m2)], gch.size) ∧ 2exp-size(# gch.ar) ∧ heap-order(gch.ar, gch.size) ↔ bin-heap-inv(gch, lpt)

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[n, mklp(n0, n1, lpf1, m2)], gch] flags: <all paths>

Additional information

Used terms: lpt[n, mklp(n0, n1, lpf1, m2)], gch