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Proof step 2 from proof transaction-prefix-last-nonend (previous step)

transaction-prefix(ndx, gndx + mkgnode(nd, n, boolvar, true) ') ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
(gndx + mkgnode(nd, n, boolvar, true) ').head.start, # gndx + 1 < # ndx, ∀ n0. ¬ # gndx < n0 → (gndx + mkgnode(nd, n, boolvar, true) ')[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gndx + mkgnode(nd, n, boolvar, true) ')[n0].start) ∧ (¬ # gndx < n0 → ¬ (gndx + mkgnode(nd, n, boolvar, true) ')[n0].end) ⊦ ndx = []

Rule argument

Additional information

Used simplifier rules: 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]);% ⊦ # ndx = 0 ↔ ndx = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ gndx + gnd ' ≠ []; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)