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Proof step 11 from proof binheap-inv-remove-wbufs (previous step)

2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, lpt, m), m ≤ # kar ⊦ valid-idx(kar, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ valid-idx(kar, lpt, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # lpt ∧ lpt[kar[m].idx].gcheapidx = m)
Proof step 13:
2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, lpt, m), m ≤ # kar ⊦ m ≤ # kar ∧ (∀ m0. m0 < m → kar[m0].idx < # lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE) ∧ lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[kar[m0].idx].gcheapidx = m0)

Rule argument

spec: bin-min-heap-inv, inst: gc-heap-rename-gc-heap-base name: valid-idx seq: ⊦ valid-idx(kar, lpt, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # lpt ∧ lpt[kar[m].idx].gcheapidx = m) subst: [n, lpt, kar] → [m, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), kar] flags: <all paths>

Additional information

Used terms: m, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), kar