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Proof step 16 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, (mkgnode(nd, m, true, boolvar0) ' + prefixn(n - # mkgnode(nd, m, true, boolvar0) ', gndx0)).head = mkgnode(nd1, m1, boolvar2, boolvar3), (mkgnode(nd, m, true, boolvar0) ' + gndx0).last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(n - # mkgnode(nd, m, true, boolvar0) ', gndx0))[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + prefixn(n - # mkgnode(nd, m, true, boolvar0) ', gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), n < # ndx, n ≤ # gndx0, # mkgnode(nd, m, true, boolvar0) ' ≤ n, ∀ 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] ⊦ n = 0, ndx = [], boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# 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)

Rule argument

Additional information

Used simplifier rules: ⊦ gndx ≠ [] → (gnd ' + gndx).last = gndx.last; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ (gnd ' + gndx).head = gnd; (s)% ⊦ # gnd ' = 0 +1; (s)