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Proof step 5 from proof valid-wl-next-bad (previous step)

# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m < # wlar, ∀ n. n < m → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ (∀ n. ¬ m < n → (wlar[m, wl-entry(m0, erroneous)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[m, wl-entry(m0, erroneous)][n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = (valid-sqns(v, m1, apebs, m) ∪ (valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m2, boolvar)) ⊃ {avhdr.sqn} ;∅)).max))) ↔ boolvar

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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