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Proof step 18 from proof transaction-prefix-app (previous step)

gndx0.head = mkgnode(nd1, m1, true, boolvar4), gndx0[n0] = mkgnode(nd, m, boolvar, boolvar0), gndx0[n] = mkgnode(nd2, m2, boolvar5, boolvar6), # gndx0 + # gndx1 < # ndx, # gndx0 < # ndx, ∀ n. (n ≠ 0 ∧ n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].start) ∧ (n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].end), ∀ n. n < # gndx0 + # gndx1 → (gndx0 + gndx1)[n].nd = ndx[n] ⊦ gndx0 + gndx1 = [], gndx0 = [], ndx = [], (n < # gndx0 → ¬ boolvar6) ∧ (n ≠ 0 ∧ n < # gndx0 → ¬ boolvar5)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
gndx0[n] = mkgnode(nd2, m2, boolvar5, boolvar6), gndx0[n0] = mkgnode(nd, m, boolvar, boolvar0), gnd = mkgnode(nd1, m1, true, boolvar4), gndx0 = gnd + gndx2, # gndx0 < # ndx, # gndx0 + # gndx1 < # ndx, ∀ n. n < # gndx0 + # gndx1 → (gndx0 + gndx1)[n].nd = ndx[n], ∀ n. (n ≠ 0 ∧ n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].start) ∧ (n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].end) ⊦ gndx0 + gndx1 = [], gndx0 = [], ndx = [], (n < # gndx0 → ¬ boolvar6) ∧ (n ≠ 0 ∧ n < # gndx0 → ¬ boolvar5)

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] → [gndx0, gnd, gndx]

Additional information

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