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Proof step 11 from proof abs-idset-fwd (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
# 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 ⊦ vols[v][m] = unmapped, buf0 = buf ∧ m0 ≤ m1

Rule argument

spec: ebaentry name: elim seq: ⊦ ebae ≠ unmapped → (m = ebae.pnum ↔ ebae = ⌜m⌝ ) subst: [ebae, m] → [vols[v][m], m3]

Additional information

Used simplifier rules: ⊦ ebae ≠ unmapped → (m = ebae.pnum ↔ ebae = ⌜m⌝ ); (elim) Used terms: vols[v][m], m3