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Proof step 21 from proof transaction-prefix-app (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
(mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n0] = mkgnode(nd, m, boolvar, boolvar0), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n] = mkgnode(nd2, m2, boolvar5, true), (# gndx2 + 1) + # gndx1 < # ndx, # gndx2 + 1 < # ndx, n ≤ # gndx2, ∀ 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), ∀ n1. ¬ # gndx2 + # gndx1 < n1 → ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].nd = ndx[n1] ⊦ ndx = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)