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Proof step 2 from proof transaction-prefix-is-transaction-prefix (previous step)

n < # gndx, transaction(ndx, gndx) ⊦ transaction-prefix(ndx, prefixn(n, gndx))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# 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])

Rule argument

Additional information

Used simplifier rules: transaction: ⊦ transaction(ndx, gndx) ↔ # gndx = # ndx ∧ ( gndx = [] ∨ gndx.head.start ∧ gndx.last.end ∧ (∀ n. (0 < n ∧ n < # gndx → ¬ gndx[n].start) ∧ (n + 1 < # gndx → ¬ gndx[n].end))) ∧ (∀ n. n < # gndx → gndx[n].nd = ndx[n]);%transaction-prefix: ⊦ transaction-prefix(ndx, gndx) ↔ # gndx < # ndx ∧ ( gndx = [] ∨ gndx.head.start ∧ (∀ n. (0 < n ∧ n < # gndx → ¬ gndx[n].start) ∧ (n < # gndx → ¬ gndx[n].end))) ∧ (∀ n. n < # gndx → gndx[n].nd = ndx[n]);% ⊦ # [] = 0; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ m < n → m ≤ n; (s)%n ≤ # gndx ⊦ # prefixn(n, gndx) = n; (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 0 < m ↔ m ≠ 0; (s)