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Proof step 44 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0).head = mkgnode(nd1, m1, boolvar2, boolvar3), (mkgnode(nd, m, true, boolvar0) ' + gndx0).last = mkgnode(nd3, m3, boolvar6, true), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n1 < n, n < # ndx, 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] ⊦ nd0 = ndx[n1], ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ n < n0 → (n0 < n ↔ false); (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx ≠ [] → (gnd ' + gndx).last = gndx.last; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic