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Proof step 5 from proof transaction-prefix-last-nonend (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
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 = []

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] → [gnd, nd0, m, boolvar0, boolvar1]

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: gnd, nd0, m, boolvar0, boolvar1