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Proof step 18 from proof absexpt-idset (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 19:
# 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, v0 ≠ v ∨ m0 ≠ m ⊦ buf0 = buf ∧ m1 ≤ m2, m4 ≠ n ∧ m4 ∈ mapped-pebs(vols) ∧ m4 < # apebs0

Rule argument

pos: left 15

Proof step 18 from proof absexpt-idset (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information