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Proof step 47 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0).head = mkgnode(nd1, m1, boolvar2, boolvar3), gndx0.last = mkgnode(nd3, m3, boolvar6, true), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n1 < # gndx0, n1 < # ndx, n < # ndx, n1 < n, n1 < #(mkgnode(nd, m, true, boolvar0) ' + gndx0), 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] ⊦ gndx0 = [], nd0 = ndx[n1], ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# gndx0 + 1 = # ndx, prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0).head = mkgnode(nd1, m1, boolvar2, boolvar3), gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), n1 < n, n < # ndx, n1 < # ndx, n1 < # gndx0, n ≤ # 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) ⊦ gndx0 = [], nd0 = ndx[n1], ndx = []

Rule argument

Additional information

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