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Proof step 18 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n = m1 + 1, n < # ndx, 1 ≤ # gndx0, 1 ≤ n, n ≤ # gndx0, ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end), ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n = 0, ndx = [], (n0 < n → ¬ boolvar5) ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), m1 < # gndx0, 1 ≤ # gndx0, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2], ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end) ⊦ # ndx = 1, gndx0 = [], ndx = [], (¬ m1 < n0 → ¬ boolvar5) ∧ (n0 ≠ 0 ∧ ¬ m1 < n0 → ¬ boolvar4)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ m ≤ m + n; (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)