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Proof step 19 from proof abs-idset-fwd (previous step)

# 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 ⊦ buf0 = buf ∧ m0 ≤ m1, m3 ∈ mapped-pebs(vols) ∧ m3 < # apebs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ n ∈ mapped-pebs(vols) ↔ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )
Proof step 21:
# vols[v] = # avols[v], # apebs1 = # apebs0, 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], valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v ∈ avols, m2 ≤ m1 ⊦ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜m3⌝ ) ∧ m3 < # apebs0, buf0 = buf ∧ m0 ≤ m1

Rule argument

spec: ubi-base name: mapped-pebs seq: ⊦ n ∈ mapped-pebs(vols) ↔ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ) subst: [vols, n] → [vols, m3] flags: <all paths>

Additional information

Used terms: vols, m3