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Proof step 3 from proof remove-wbufs-rec (previous step)

⊦ lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE) = lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n].size:= LEB_SIZE], n ∈ ns

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ lpt = lpt0 ↔ # lpt = # lpt0 ∧ (∀ n. n < # lpt → lpt[n] = lpt0[n])
Proof step 5:
⊦ n ∈ ns, # lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE) = # lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n].size:= LEB_SIZE] ∧ (∀ n0. n0 < # lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE) → lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE)[n0] = lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n].size:= LEB_SIZE][n0])

Rule argument

spec: array, inst: lp-array name: Extension seq: ⊦ lpt = lpt0 ↔ # lpt = # lpt0 ∧ (∀ n. n < # lpt → lpt[n] = lpt0[n]) subst: [lpt0, lpt] → [lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE) [n, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n] .size:= LEB_SIZE ], lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE)] flags: <all paths>

Additional information

Used terms: lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE) [n, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n].size:= LEB_SIZE ], lpt.mapIndices(ns ++ n, λ lp. lp.size:= LEB_SIZE)