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Proof step 42 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), gndx0[n0 - # mkgnode(nd, m, true, boolvar0) '] = mkgnode(nd1, m4, false, false), (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), n0 < # ndx, m1 < # gndx0, n0 < # gndx0, 1 ≤ # gndx0, n0 ≤ m1, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n0 = 0, ndx = [], n0 < # mkgnode(nd, m, true, boolvar0) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), prefixn(m1, gndx0)[n0 - 1] = mkgnode(nd2, m2, true, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), gndx0[n0 - 1] = mkgnode(nd1, m4, false, false), n0 < # gndx0, m1 < # gndx0, n0 < # ndx, n0 ≤ m1, 1 ≤ # gndx0, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n0 = 0, ndx = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx]; (s)