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Proof step 39 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode((ndx + nd ')[0], m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), mkgnode(nd, n, false, true) ∈ gndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = ndx.head, ndx = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
# ndx = # gndx, gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode((ndx + nd ')[0], m1, true, boolvar4), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), ndx = nd0 + ndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, mkgnode(nd, n, false, true) ∈ gndx0, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = nd0, ndx = []

Rule argument

spec: list-data, inst: node-list name: elim-list-c seq: ndx ≠ [] ⊦ nd = ndx.head ∧ ndx0 = ndx.tail ↔ ndx = nd + ndx0 subst: [ndx, nd, ndx0] → [ndx, nd0, ndx0]

Additional information

Used simplifier rules: ndx ≠ [] ⊦ nd = ndx.head ∧ ndx0 = ndx.tail ↔ ndx = nd + ndx0; (elim) Used terms: ndx, nd0, ndx0