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

# 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 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# ndx = # gndx1 + 1, gndx1[m3] = mkgnode(nd2, m1, boolvar, boolvar3), (gndx1 + mkgnode(nd, n, false, false) ')[m3] = mkgnode(nd3, m2, true, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, false, false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), m3 < # ndx, m3 ≤ # gndx1, m3 < # gndx1 → ¬ boolvar3, m3 < # gndx1 → ¬ boolvar, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ' + ndx1)[n2] ⊦ ndx = [], ndx1 = []

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)