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Proof step 3 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx = # ndx, gndx.last.end, gndx.head.start, n < # ndx, ∀ n. n < # ndx → gndx[n].nd = ndx[n], ∀ n0. (n0 ≠ 0 ∧ n0 < # ndx → ¬ gndx[n0].start) ∧ (n0 + 1 < # ndx → ¬ gndx[n0].end) ⊦ gndx = [], ndx = [], ( prefixn(n, gndx) = [] ∨ prefixn(n, gndx).head.start ∧ (n0 ≠ 0 ∧ n0 < n → ¬ prefixn(n, gndx)[n0].start) ∧ (n0 < n → ¬ prefixn(n, gndx)[n0].end)) ∧ (n1 < n → prefixn(n, gndx)[n1].nd = ndx[n1])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# gndx = # ndx, gndx = gnd + gndx0, gndx.last.end, gnd.start, n < # ndx, ∀ n0. (n0 ≠ 0 ∧ n0 < # ndx → ¬ gndx[n0].start) ∧ (n0 + 1 < # ndx → ¬ gndx[n0].end), ∀ n. n < # ndx → gndx[n].nd = ndx[n] ⊦ gndx = [], ndx = [], ( prefixn(n, gndx) = [] ∨ prefixn(n, gndx).head.start ∧ (n0 ≠ 0 ∧ n0 < n → ¬ prefixn(n, gndx)[n0].start) ∧ (n0 < n → ¬ prefixn(n, gndx)[n0].end)) ∧ (n1 < n → prefixn(n, gndx)[n1].nd = ndx[n1])

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, gndx0]

Additional information

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