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Proof step 30 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0 ⊦ nd1 = (ndx + nd ')[n1], # gndx < n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), n1 ≤ # gndx, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true) ⊦ nd1 = (ndx + nd ')[n1]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)