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Proof step 6 from proof freelist-cons-remove-wbufs (previous step)

n < # lpt ∧ lpf0 = LP_FREE ↔ n ∈ freelist, lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n] = mklp(m, m0, lpf, m1), lpt[n] = mklp(m2, m3, lpf0, m4) ⊦ n < # lpt ∧ lpf = LP_FREE ↔ n ∈ freelist, dups(freelist)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 8:
(n ∈ ns ∧ n < # lpt ⊃ lpt[n].size:= LEB_SIZE;lpt[n]) = mklp(m, m0, lpf, m1), n < # lpt ∧ lpf0 = LP_FREE ↔ n ∈ freelist, lpt[n] = mklp(m2, m3, lpf0, m4) ⊦ n < # lpt ∧ lpf = LP_FREE ↔ n ∈ freelist, dups(freelist)

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] → [n, λ lp. lp.size:= LEB_SIZE, ns, lpt] flags: <all paths>

Additional information

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