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Proof step 13 from proof absexpt-idset (previous step)

# vols[v0] = # avols[v0], apebs0[m4] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), vols[v][m] = ⌜n⌝ , apebs1[m4] = mkpeb(aehdr, avhdr, buf, m1, boolvar), avols[v0][m0] = mapped(buf0, m2), vols[v0][m0] = ⌜m4⌝ , m < # vols[v], m0 < # avols[v0], id(apebs1, apebs0, mapped-pebs(vols) -- n), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v0 ∈ vols, v0 ∈ avols, m3 ≤ m2, v0 ≠ v ∨ m0 ≠ m ⊦ buf0 = buf ∧ m1 ≤ m2

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[v0] = # avols[v0], vols[v0][m0] = ⌜m4⌝ , avols[v0][m0] = mapped(buf0, m2), apebs1[m4] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , apebs0[m4] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), m0 < # avols[v0], m < # vols[v], valid-ebatbl(apebs0, wlar, vols, n0), v0 ∈ avols, v0 ∈ vols, v ∈ vols, m3 ≤ m2, ∀ n0. n0 ∈ mapped-pebs(vols) -- n ∧ n0 < # apebs1 ∧ n0 < # apebs0 → apebs1[n0] = apebs0[n0], v0 ≠ v ∨ m0 ≠ m ⊦ buf0 = buf ∧ m1 ≤ m2

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) -- n, apebs0, apebs1] flags: <all paths>

Additional information

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