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Proof step 15 from proof absexpt-idset (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# 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, ∀ n1. n1 ≠ n ∧ n1 ∈ mapped-pebs(vols) ∧ n1 < # apebs0 → apebs1[n1] = apebs0[n1], v0 ≠ v ∨ m0 ≠ m ⊦ buf0 = buf ∧ m1 ≤ m2

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)