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Proof step 53 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, gndx1[n1 - 1] = mkgnode(ndx[n1], m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1 - 1] = mkgnode(nd1, m0, boolvar1, boolvar2), n1 ≤ # gndx1, ∀ n2. (n2 ≠ 0 ∧ ¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].start) ∧ (¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].end) ⊦ n1 = 0, nd1 = ndx[n1], ndx1 = []

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n1, m1]

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ n < # gndx → (gndx + gnd ')[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n1, m1