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Proof step 14 from proof valid-vtbl-map-indices-erasing (previous step)

avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar[m] = wl-entry(m1, used), apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar), wlar.mapIndices(nx, f)[m] = wl-entry(m2, stat), m < # apebs, m < # wlar, indices-erasing(wlar, nx), is-encoded(to-vtbl(vols), buf), valid-indices(wlar, nx) ⊦ dups(nx), m < # wlar.mapIndices(nx, f) ∧ stat = used

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n])
Proof step 16:
avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, (m ∈ nx ⊃ f(wlar[m]);wlar[m]) = wl-entry(m2, stat), apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar), wlar[m] = wl-entry(m1, used), m < # apebs, m < # wlar, indices-erasing(wlar, nx), is-encoded(to-vtbl(vols), buf), valid-indices(wlar, nx) ⊦ dups(nx), m < # wlar.mapIndices(nx, f) ∧ stat = used

Rule argument

spec: array-indices, inst: wlarray-base name: map-indices-at seq: ⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n]) subst: [n, f0, nx, wlar] → [m, f, nx, wlar] flags: <all paths>

Additional information

Used terms: m, f, nx, wlar