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

# ndx = # gndx1 + 1, (gndx1 + mkgnode(nd, n, ndx = [], true) ')[n0 - 1] = mkgnode(nd3, m2, true, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], true) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), gndx1[n0 - 1] = mkgnode(nd4, m3, boolvar7, boolvar8), n0 ≤ # ndx, ¬ # gndx1 < n0 → ¬ boolvar7, ¬ # gndx1 < n0 → ¬ boolvar8, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ')[n2] ⊦ n0 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# ndx = # gndx1 + 1, gndx1[m1] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], true) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (gndx1 + mkgnode(nd, n, ndx = [], true) ')[m1] = mkgnode(nd3, m2, true, boolvar6), n0 = m1 + 1, n0 ≤ # ndx, ¬ # gndx1 < n0 → ¬ boolvar8, ¬ # gndx1 < n0 → ¬ boolvar7, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ')[n2] ⊦ n0 = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n0, m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n0, m1