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Proof step 31 from proof transaction-prefix-app (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
(mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n0] = mkgnode(nd, m, boolvar, boolvar0), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n] = mkgnode(nd2, m2, true, boolvar6), ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n] = mkgnode(nd0, m0, boolvar1, boolvar2), ¬ boolvar1, ¬ boolvar2, (# gndx2 + 1) + # gndx1 < # ndx, # gndx2 + 1 < # ndx, n ≤ # gndx2 + # gndx1, n ≤ # gndx2, ∀ n1. ¬ # gndx2 + # gndx1 < n1 → ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].nd = ndx[n1] ⊦ n = 0, ndx = []

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n], nd0, m0, boolvar1, boolvar2]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n], nd0, m0, boolvar1, boolvar2