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Proof step 15 from proof valid-wl-markbad (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m1, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), wlar[n] = wl-entry(m5, used), m < # wlar, n < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)) ⊦ avhdr0.sqn = (valid-sqns(v, m1, apebs) \ (valid-peb(v, m1, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)).max, n = m

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 16:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m1, apebs).max, wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), n < # wlar, m < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)), valid-peb(v, m1, apebs[m]) ⊦ avhdr0.sqn = (valid-sqns(v, m1, apebs) \ {apebs[m].vidhdr.sqn} ).max, n = m

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ bag \ ∅ = bag; (s)