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Proof step 23 from proof transaction-prefix-app-last (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# ndx = # gndx1 + 1, gndx1[m1] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, false, true) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (gndx1 + mkgnode(nd, n, false, true) ')[m1] = mkgnode(nd3, m2, true, boolvar6), m1 < # ndx, m1 ≤ # gndx1, m1 < # gndx1 → ¬ boolvar8, m1 < # gndx1 → ¬ boolvar7, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ')[n2] ⊦ ndx = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # ndx = 0 ↔ ndx = []; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)