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Proof step 17 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(n - 1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), (mkgnode(nd, m, true, boolvar0) ' + prefixn(n - 1, gndx0))[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), n < # ndx, n ≤ # gndx0, 1 ≤ n, 1 ≤ # gndx0, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2], ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end) ⊦ # ndx = 1, gndx0 = [], n = 0, ndx = [], (n0 < n → ¬ boolvar5) ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n = m1 + 1, n < # ndx, 1 ≤ # gndx0, 1 ≤ n, n ≤ # gndx0, ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end), ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n = 0, ndx = [], (n0 < n → ¬ boolvar5) ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4)

Rule argument

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

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m