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Proof step 6 from proof transaction-prefix-last-nonend (previous step)

gndx + mkgnode(nd, n, boolvar, true) ' = gnd ' + gndx0, boolvar0, gnd = mkgnode(nd0, m, boolvar0, boolvar1), # gndx + 1 < # ndx, ∀ n0. ¬ # gndx < n0 → (gnd ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (¬ # gndx < n0 → ¬ (gnd ' + gndx0)[n0].end), gnd ∈ gndx ∨ gnd = mkgnode(nd, n, boolvar, true), mkgnode(nd, n, boolvar, true) = gnd ∨ mkgnode(nd, n, boolvar, true) ∈ gndx0 ⊦ ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
gndx + mkgnode(nd, n, boolvar, true) ' = mkgnode(nd0, m, true, boolvar1) ' + gndx0, # gndx + 1 < # ndx, ∀ n0. ¬ # gndx < n0 → (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].start) ∧ (¬ # gndx < n0 → ¬ (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].end), mkgnode(nd, n, boolvar, true) = mkgnode(nd0, m, true, boolvar1) ∨ mkgnode(nd, n, boolvar, true) ∈ gndx0, mkgnode(nd0, m, true, boolvar1) ∈ gndx ∨ mkgnode(nd0, m, true, boolvar1) = mkgnode(nd, n, boolvar, true) ⊦ ndx = []

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]