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Proof step 8 from proof valid-recs-sqns-update (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m0 < # apebs, ladr ∈ recs[v × m, recovery-entry(m0, avhdr.sqn)], ∀ ladr. ladr ∈ recs → recs[ladr].pnum < # apebs ∧ apebs[recs[ladr].pnum].vidhdr.sqn = recs[ladr].sqn ⊦ recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr].pnum < # apebs ∧ apebs[recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr].pnum].vidhdr.sqn = recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr].sqn

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr] = recovery-entry(m1, m3), m0 < # apebs, ladr ∈ recs[v × m, recovery-entry(m0, avhdr.sqn)], ∀ ladr. ladr ∈ recs → recs[ladr].pnum < # apebs ∧ apebs[recs[ladr].pnum].vidhdr.sqn = recs[ladr].sqn ⊦ m1 < # apebs ∧ apebs[m1].vidhdr.sqn = m3

Rule argument

spec: recovery-entry name: elim seq: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0) subst: [rec, m, m0] → [recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr], m1, m3]

Additional information

Used simplifier rules: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0); (elim) Used terms: recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr], m1, m3