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Proof step 25 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd1, m4, boolvar2, 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, boolvar4, true), m1 < # gndx0, n0 < # gndx0, 1 ≤ # gndx0, n0 ≤ m1, n0 ≠ 0 ∧ n0 < # ndx → ¬ boolvar2, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], ndx = []

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 26:
# gndx0 + 1 = # ndx, gndx0.last = mkgnode(nd3, m3, boolvar6, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n0] = mkgnode(nd2, m2, boolvar4, true), (mkgnode(nd, m, true, boolvar0) ' + prefixn(m1, gndx0))[n1] = mkgnode(nd0, m0, boolvar, boolvar1), (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd1, m4, boolvar2, false), n0 < # gndx0, m1 < # gndx0, n0 ≤ m1, 1 ≤ # gndx0, n0 ≠ 0 ∧ n0 < # ndx → ¬ boolvar2, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ # ndx = 1, gndx0 = [], n0 = 0, ndx = []

Rule argument

fma: n0 = 0

Additional information

Used simplifier rules: ⊦ (gnd ' + gndx)[0] = gnd; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws) Used formulas: n0 = 0