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Proof step 23 from proof binheap-inv-remove-wbufs (previous step)

kar[m6] = key-index(natkey, m4), lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[m4] = mklp(m1, m2, lpf, m3), lpt[m4] = mklp(m0, m5, lpf0, m6), 2exp-size(# kar), m6 < # kar, m6 < m, m4 < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = m6

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 25:
(m4 ∈ ns ∧ m4 < # lpt ⊃ lpt[m4].size:= LEB_SIZE;lpt[m4]) = mklp(m1, m2, lpf, m3), lpt[m4] = mklp(m0, m5, lpf0, m6), kar[m6] = key-index(natkey, m4), 2exp-size(# kar), m4 < # lpt, m6 < m, m6 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = m6

Rule argument

spec: array-indices, inst: lp-array name: mapindices-at seq: ⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n]) subst: [n, lptfun, ns, lpt] → [m4, λ lp. lp.size:= LEB_SIZE, ns, lpt] flags: <all paths>

Additional information

Used terms: m4, λ lp. lp.size:= LEB_SIZE, ns, lpt