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Proof step 6 from proof MAIN-example (previous step)

P = pe(0, 2, 0) ' + pe(3, 5, 0) ', D = (∅)[100, 2][11, 5][22, 0][33, 1][44, 4][55, 3], A = mkarray(6)[0, 22][1, 33][2, 100][3, 55][4, 44][5, 11], F = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1] ⊦ ⟨REFINE(11 ' + 22 ' + 44 ', F; A, D, P)⟩ ⟨NEWPARTS(; P, F)⟩ ( A = mkarray(6)[0, 22][1, 33][2, 100][3, 11][4, 44][5, 55] ∧ D = (∅)[100, 2][11, 3][22, 0][33, 1][44, 4][55, 5] ∧ P = pe(0, 0, 0) ' + pe(3, 4, 0) ' + pe(1, 2, 0) ' + pe(5, 5, 0) ' ∧ F = (∅)[0, 0][1, 2][2, 2][3, 1][4, 1][5, 3])

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name:REFINE-example seq: A = mkarray(6)[0, 22][1, 33][2, 100][3, 55][4, 44] [5, 11 ], D = (∅)[100, 2][11, 5][22, 0][33, 1][44, 4][55, 3], P = pe(0, 2, 0) + pe(3, 5, 0) + [], X = 11 + 22 + 44 + [], F = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1] ⊦ ⟨REFINE(X, F; A, D, P)⟩ ( A = mkarray(6)[0, 22][1, 33][2, 100][3, 11] [4, 44 ] [5, 55 ] ∧ D = (∅)[100, 2][11, 3][22, 0][33, 1][44, 4] [55, 5 ] ∧ P = pe(0, 2, 1) + pe(3, 5, 2) + []) subst:[A, D, P, X, F] → [A, D, P, 11 ' + 22 ' + 44 ', F] flags:current, []

Additional information

[Concretesimprules((Csimpnamedseq(list,partition,c, ⊦ p + P = p ' + P) Csimpnamedseq(list,partition,app, ⊦ P + [] = P) Csimpnamedseq(list,partition,a, ⊦ (P + P0) + P1 = P + P0 + P1) Csimpnamedseq(list,partition,app-01, ⊦ P + P0 = P + P1 ↔ P0 = P1) Csimpnamedseq(list,list_of_nat,c, ⊦ n + X = n ' + X) Csimpnamedseq(list,list_of_nat,app, ⊦ X + [] = X) Csimpnamedseq(list,list_of_nat,a, ⊦ (X + X0) + X1 = X + X0 + X1) Csimpnamedseq(list,list_of_nat,app-01, ⊦ X + X0 = X + X1 ↔ X0 = X1))), Extraterms((ADP11 ' + 22 ' + 44 'F))]