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Proof step 77 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], 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) ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
D1 = (∅)[100, 2][11, 5][22, 0][33, 1][44, 4][55, 3], A1 = mkarray(6)[0, 22][1, 33][2, 100][3, 55][4, 44][5, 11], P1 = pe(0, 2, 0) ' + pe(3, 5, 0) ' ⊦ ⟨REFINEONE(11, (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1]; A1, D1, P1)⟩ ⟨X0 := 22 ' + 44 '⟩ ⟨F0 := (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1]; 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

Additional information

[Concretesimprules((Csimpnamedseq(list,list_of_nat,in-17, ⊦ n ∈ n0 ' ↔ n = n0) Csimpnamedseq(list,list_of_nat,in-append, ⊦ n ∈ X + X0 ↔ ¬ ¬(n ∈ X ∨ n ∈ X0)) Csimpnamedforward(list,list_of_nat,in-14, ⊦ n ' + X = X0 → n ∈ X0) Csimpnamedforward(list,list_of_nat,in-15, ⊦ X + n ' = X0 → n ∈ X0) Csimpnamedseq(list,list_of_nat,c-07, ⊦ (n ' + X).tail = X) Csimpnamedseq(list,list_of_nat,e-01, ⊦ n ' + X ≠ []) Csimpnamedseq(list,list_of_nat,a, ⊦ (X + X0) + X1 = X + X0 + X1) Csimpnamedseq(list,list_of_nat,c-06, ⊦ n ' + X = n0 ' + X0 ↔ n = n0 ∧ X = X0) Csimpnamedseq(list,list_of_nat,c, ⊦ n + X = n ' + X)))]