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Proof step 40 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode((ndx + nd ')[0], m1, true, boolvar4), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), ndx = nd0 + ndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, mkgnode(nd, n, false, true) ∈ gndx0, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = nd0, ndx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, # ndx0 + 1 = # gndx, gndx.head = mkgnode(nd0, m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), mkgnode(nd, n, false, true) ∈ gndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = nd0

Rule argument

Additional information

Used simplifier rules: ⊦ nd ' + ndx ≠ []; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(nd ' + ndx) = (# ndx)+1; (s)% ⊦ (nd ' + ndx)[0] = nd; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ nd + ndx = nd ' + ndx; (s)