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Proof step 35 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(m1, gndx0))[n0] = mkgnode(nd2, m2, true, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n0 < # gndx0, m1 < # gndx0, n0 ≤ m1, 1 ≤ # gndx0, n0 ≠ 0 ∧ n0 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0].start, n0 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0].end, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n0 = 0, ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n0] = mkgnode(nd2, m2, true, boolvar5), m1 < # gndx0, n0 < # gndx0, 1 ≤ # gndx0, n0 ≤ m1, n0 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0].start, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n0 = 0, ndx = [], (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0].end

Rule argument

Additional information

Used simplifier rules: ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic