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Proof step 13 from proof abs-idset-fwd (previous step)

# vols[v] = # avols[v], apebs0[m3] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs1[m3] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avols[v][m] = mapped(buf0, m1), vols[v][m] = ⌜m3⌝ , m < # avols[v], id(apebs1, apebs0, mapped-pebs(vols)), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v ∈ avols, m2 ≤ m1 ⊦ buf0 = buf ∧ m0 ≤ m1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ id(apebs0, apebs1, ns) ↔ # apebs0 = # apebs1 ∧ (∀ n. n ∈ ns ∧ n < # apebs0 ∧ n < # apebs1 → apebs0[n] = apebs1[n])
Proof step 15:
# apebs1 = # apebs0, # vols[v] = # avols[v], vols[v][m] = ⌜m3⌝ , avols[v][m] = mapped(buf0, m1), apebs1[m3] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs0[m3] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m < # avols[v], valid-ebatbl(apebs0, wlar, vols, n0), v ∈ avols, v ∈ vols, m2 ≤ m1, ∀ n. n ∈ mapped-pebs(vols) ∧ n < # apebs1 ∧ n < # apebs0 → apebs1[n] = apebs0[n] ⊦ buf0 = buf ∧ m0 ≤ m1

Rule argument

spec: ubi-base name: id-set seq: ⊦ id(apebs0, apebs1, ns) ↔ # apebs0 = # apebs1 ∧ (∀ n. n ∈ ns ∧ n < # apebs0 ∧ n < # apebs1 → apebs0[n] = apebs1[n]) subst: [ns, apebs1, apebs0] → [mapped-pebs(vols), apebs0, apebs1] flags: <all paths>

Additional information

Used terms: mapped-pebs(vols), apebs0, apebs1