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Proof step 10 from proof valid-recs-sqns-update (previous step)

recs[v × m, recovery-entry(m0, avhdr.sqn)][ladr] = recovery-entry(m1, m3), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), apebs[m1] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), 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 ∧ avhdr0.sqn = m3

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 11:
apebs[m1] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), 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 ⊦ ladr = v × m, m1 < # apebs ∧ avhdr0.sqn = m3

Rule argument

fma: ladr = v × m

Additional information

Used simplifier rules: ⊦ recs[ladr, rec][ladr] = rec; (s)% ⊦ recovery-entry(m, m0) = recovery-entry(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ ladr ∈ recs[ladr, rec]; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s) Used formulas: ladr = v × m