float_rmat_of_eulers_312_ensures_2.json 2.72 KB
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[ { "header": "Definition", "tactic": "Wp.unfold", "params": {},
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    "select": { "select": "inside-goal", "occur": 0,
                "target": "let a_0 = (shiftfield_F9_FloatRMat_m rm_0) in\nlet r_0 = Mf32_9[(shiftfield_F10_FloatEulers_phi e_1)] in\nlet r_1 = (\\sin r_0) in\nlet r_2 = Mf32_9[(shiftfield_F10_FloatEulers_psi e_1)] in\nlet r_3 = (\\sin r_2) in\nlet r_4 = Mf32_9[(shiftfield_F10_FloatEulers_theta e_1)] in\nlet r_5 = (\\sin r_4) in\nlet r_6 = (\\cos r_2) in\nlet r_7 = (\\cos r_4) in\nlet r_8 = (\\cos r_0) in\n(L_l_RMat_of_FloatRMat\n  Mf32_9[(shift_float32 a_0 0)->(r_6*r_7)-(r_1*r_3*r_5)]\n    [(shift_float32 a_0 1)->(r_3*r_7)+(r_1*r_5*r_6)][(shift_float32 a_0 2)\n    ->-1*r_5*r_8][(shift_float32 a_0 3)->-1*r_3*r_8][(shift_float32 a_0 4)\n    ->r_8*r_6][(shift_float32 a_0 5)->r_1][(shift_float32 a_0 6)\n    ->(r_5*r_6)+(r_1*r_3*r_7)][(shift_float32 a_0 7)\n    ->(r_3*r_5)-(r_1*r_6*r_7)][(shift_float32 a_0 8)->r_8*r_7] rm_0)",
                "pattern": "L_l_RMat_of_FloatRMat[=]$rm[=]shift_float32" },
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    "children": { "Unfold 'L_l_RMat_of_FloatRMat'": [ { "header": "Definition",
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                                                        "tactic": "Wp.unfold",
                                                        "params": {},
                                                        "select": { "select": "clause-goal",
                                                                    "target": "let r_0 = Mf32_9[(shiftfield_F10_FloatEulers_phi e_1)] in\nlet r_1 = (\\sin r_0) in\nlet r_2 = Mf32_9[(shiftfield_F10_FloatEulers_psi e_1)] in\nlet r_3 = (\\sin r_2) in\nlet r_4 = Mf32_9[(shiftfield_F10_FloatEulers_theta e_1)] in\nlet r_5 = (\\sin r_4) in\nlet r_6 = (\\cos r_2) in\nlet r_7 = (\\cos r_4) in\nlet r_8 = (\\cos r_0) in\n(P_special_orthogonal\n  {\n     F12_RealRMat_s_a00 = (r_6*r_7)-(r_1*r_3*r_5) ;\n     F12_RealRMat_s_a01 = (r_3*r_7)+(r_1*r_5*r_6) ;\n     F12_RealRMat_s_a02 = -1*r_5*r_8 ;\n     F12_RealRMat_s_a10 = -1*r_3*r_8 ;\n     F12_RealRMat_s_a11 = r_8*r_6 ;\n     F12_RealRMat_s_a12 = r_1 ;\n     F12_RealRMat_s_a20 = (r_5*r_6)+(r_1*r_3*r_7) ;\n     F12_RealRMat_s_a21 = (r_3*r_5)-(r_1*r_6*r_7) ;\n     F12_RealRMat_s_a22 = r_8*r_7\n  })",
                                                                    "pattern": "P_special_orthogonal{RealRMat_s}" },
                                                        "children": { "Unfold 'P_special_orthogonal'": 
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                                                                    [ { "prover": "Alt-Ergo:2.3.3",
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                                                                    "verdict": "valid",
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                                                                    "time": 2.004,
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                                                                    "steps": 102 } ] } } ] } } ]