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Proof step 12 from proof transaction-prefix-app (previous step)

(mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n0] = mkgnode(nd, m, boolvar, boolvar0), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n] = mkgnode(nd2, m2, boolvar5, boolvar6), (# gndx2 + 1) + # gndx1 < # ndx, # gndx2 + 1 < # ndx, n0 < # ndx, n0 + 1 < # ndx, n0 ≤ # gndx2, ¬ # gndx2 + # gndx1 < n0 → ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n0].nd = ndx[n0], ∀ n1. (n1 ≠ 0 ∧ ¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].start) ∧ (¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].end) ⊦ nd = ndx[n0], ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ 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