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Proof step 78 from proof REFINE-example (previous step)

P1 = pe(0, 2, 0) ' + pe(3, 5, 0) ', X0 = 11 ' + 22 ' + 44 ', F0 = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1], A1 = mkarray(6)[0, 22][1, 33][2, 100][3, 55][4, 44][5, 11], D1 = (∅)[100, 2][11, 5][22, 0][33, 1][44, 4][55, 3] ⊦ ⟨REFINEONE(X0.head, F0; A1, D1, P1)⟩ ⟨X0 := X0.tail⟩ ⟨while X0 ≠ [] do {REFINEONE(X0.head, F0; A1, D1, P1); X0 := X0.tail}⟩ ( A1 = mkarray(6)[0, 22][1, 33][2, 100][3, 11][4, 44][5, 55] ∧ D1 = (∅)[100, 2][11, 3][22, 0][33, 1][44, 4][55, 5] ∧ P1 = pe(0, 2, 1) ' + pe(3, 5, 2) ')

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 77:
P1 = pe(0, 2, 0) ' + pe(3, 5, 0) ', X0 = 11 ' + 22 ' + 44 ', F0 = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1], A1 = mkarray(6)[0, 22][1, 33][2, 100][3, 55][4, 44][5, 11], D1 = (∅)[100, 2][11, 5][22, 0][33, 1][44, 4][55, 3], X0 = n + X1, X0 ≠ [] ⊦ ⟨REFINEONE(n, F0; A1, D1, P1)⟩ ⟨X0 := X0.tail⟩ ⟨while X0 ≠ [] do {REFINEONE(X0.head, F0; A1, D1, P1); X0 := X0.tail}⟩ ( A1 = mkarray(6)[0, 22][1, 33][2, 100][3, 11][4, 44][5, 55] ∧ D1 = (∅)[100, 2][11, 3][22, 0][33, 1][44, 4][55, 5] ∧ P1 = pe(0, 2, 1) ' + pe(3, 5, 2) ')

Rule argument

spec:list-data inst:list_of_nat name:elim-list-c seq:X ≠ [] ⊦ n = X.head ∧ X0 = X.tail ↔ X = n + X0 subst:[X, n, X0] → [X0, n, X] flags:

Additional information

[Concretesimprules((Csimpnamedseq(list,list_of_nat,app-02-ant, ⊦ ¬ X + X0 ≠ [] ↔ X = [] ∧ X0 = []) Csimpnamedseq(list,list_of_nat,e, ⊦ n ' ≠ []) Csimpnamedseq(list,list_of_nat,a, ⊦ (X + X0) + X1 = X + X0 + X1) Csimpelim(X ≠ [] ⊦ n = X.head ∧ X0 = X.tail ↔ X = n + X0))), Extraterms((X0nX))]