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Proof step 14 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), ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n0] = mkgnode(nd0, m0, boolvar1, boolvar2), nd0 = ndx[n0], n0 + 1 < # ndx, n0 < # ndx, # gndx2 + 1 < # ndx, (# gndx2 + 1) + # gndx1 < # ndx, n0 ≤ # gndx2 + # gndx1, n0 ≤ # 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) ⊦ nd = ndx[n0], ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n0] = mkgnode(ndx[n0], m0, boolvar1, boolvar2), (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, n0 ≤ # gndx2 + # gndx1, ∀ 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 = []

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]