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Proof step 22 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0 - 1] = mkgnode(nd3, m2, true, boolvar6), gndx1[n0 - 1] = mkgnode(nd2, m1, boolvar, boolvar3), n0 ≤ # ndx, ¬ # gndx1 < n0 → ¬ boolvar, ¬ # gndx1 < n0 → ¬ boolvar3, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ' + ndx1)[n2] ⊦ n0 = 0, ndx1 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# ndx = # gndx1 + 1, gndx1[m3] = mkgnode(nd2, m1, boolvar, boolvar3), (gndx1 + mkgnode(nd, n, ndx = [], false) ')[m3] = mkgnode(nd3, m2, true, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n0 = m3 + 1, n0 ≤ # ndx, ¬ # gndx1 < n0 → ¬ boolvar3, ¬ # gndx1 < n0 → ¬ boolvar, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ' + ndx1)[n2] ⊦ n0 = 0, ndx1 = []

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n0, m3]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n0, m3