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Proof step 45 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx0[m5] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx[m5 + 1] = mkgnode(nd5, m4, boolvar9, boolvar10), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), m5 < # gndx, mkgnode(nd, n, ndx = [], true) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, m5 + 1 < # gndx → nd5 = (ndx + nd ')[m5 + 1], ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = (ndx + nd ')[m5 + 1]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: list-data, inst: group-store name: elim-list-c seq: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0 subst: [gndx, gnd, gndx0] → [gndx, gnd, gndx1]

Additional information

Used simplifier rules: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0; (elim) Used terms: gndx, gnd, gndx1