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Proof step 7 from proof valid-wl-next-bad (previous step)

# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, false), m < # wlar, ∀ 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, false)) ⊃ {avhdr.sqn} ;∅)).max)), ∀ 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)) ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ free ≠ erroneous; (s)% ⊦ used ≠ erroneous; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s) Used terms: m