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Proof step 3 from proof prepost-init-vols-sizes (previous step)

# apebs = # wlar, recs[VTBL_VOLID × VTBL_LNUM].pnum < # wlar, is-encoded(vtbl, apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum].data), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum), VTBL_VOLID × VTBL_LNUM ∈ recs ⊦ ⟪ubi_init_vols_sizes#(recs, wlar, apebs; vtbl, vols)⟫ (valid-vtbl(apebs, vols, wlar, recs[VTBL_VOLID × VTBL_LNUM].pnum) ∧ unmapped-vols(vols) ∧ ¬ VTBL_VOLID ∈ vols)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# apebs = # wlar, apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM].pnum < # wlar, is-encoded(vtbl, buf), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum), VTBL_VOLID × VTBL_LNUM ∈ recs ⊦ ⟪ubi_init_vols_sizes#(recs, wlar, apebs; vtbl, vols)⟫ (valid-vtbl(apebs, vols, wlar, recs[VTBL_VOLID × VTBL_LNUM].pnum) ∧ unmapped-vols(vols) ∧ ¬ VTBL_VOLID ∈ vols)

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum], aehdr, avhdr, buf, m, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum], aehdr, avhdr, buf, m, boolvar