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Proof step 13 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), 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] ⊦ ndx = [], prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0) = [], boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# 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)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), n < # ndx, n ≤ # gndx0, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2], ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end) ⊦ n = 0, ndx = [], boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd ' + gndx ≠ []; (s)% ⊦ prefixn(n, gndx) = [] ↔ n = 0 ∨ gndx = []; (ss)