float_quat_of_rmat_a22_max_ensures.json 11.1 KB
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[ { "header": "Definition", "tactic": "Wp.unfold", "params": {},
    "select": { "select": "inside-goal", "occur": 0,
                "target": "(L_l_FloatQuat_of_RMat_2_max_t Mf32_0 rm_0)",
                "pattern": "L_l_FloatQuat_of_RMat_2_max_t$Mf32" },
    "children": { "Unfold 'L_l_FloatQuat_of_RMat_2_max_t'": [ { "header": "Definition",
                                                                "tactic": "Wp.unfold",
                                                                "params": {},
                                                                "select": 
                                                                  { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "(L_transpose (L_l_RMat_of_FloatRMat Mf32_0 rm_0))",
                                                                    "pattern": "L_transposeL_l_RMat_of_FloatRMat" },
                                                                "children": 
                                                                  { "Unfold 'L_transpose'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-step",
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                                                                    "at": 6,
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                                                                    "kind": "have",
                                                                    "occur": 0,
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                                                                    "target": "(L_trace_2_ Mf32_2 rm_0)",
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                                                                    "pattern": "L_trace_2_$Mf32$rm" },
                                                                    "children": 
                                                                    { "Unfold 'L_trace_2_'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-step",
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                                                                    "at": 6,
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                                                                    "kind": "have",
                                                                    "occur": 0,
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                                                                    "target": "(L_trace_1_ (L_l_RMat_of_FloatRMat Mf32_2 rm_0))",
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                                                                    "pattern": "L_trace_1_L_l_RMat_of_FloatRMat$Mf32" },
                                                                    "children": 
                                                                    { "Unfold 'L_trace_1_'": 
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                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "(L_l_Quat_of_FloatQuat Mf32_0 q_0)",
                                                                    "pattern": "L_l_Quat_of_FloatQuat$Mf32$q" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_Quat_of_FloatQuat'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "let a_0 = (L_l_RMat_of_FloatRMat Mf32_0 rm_0) in\n(L_l_FloatQuat_of_RMat_2_max_1_\n  {\n     a_0 with\n     F9_RealRMat_s_a01 = a_0.F9_RealRMat_s_a10 ;\n     F9_RealRMat_s_a02 = a_0.F9_RealRMat_s_a20 ;\n     F9_RealRMat_s_a10 = a_0.F9_RealRMat_s_a01 ;\n     F9_RealRMat_s_a12 = a_0.F9_RealRMat_s_a21 ;\n     F9_RealRMat_s_a20 = a_0.F9_RealRMat_s_a02 ;\n     F9_RealRMat_s_a21 = a_0.F9_RealRMat_s_a12\n  })",
                                                                    "pattern": "L_l_FloatQuat_of_RMat_2_max_1_{RealRMat_s}" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_FloatQuat_of_RMat_2_max_1_'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "clause-goal",
                                                                    "target": "let a_0 = (L_l_RMat_of_FloatRMat Mf32_0 rm_0) in\nlet r_0 =\n    (\\sqrt\n      (1+a_0.F9_RealRMat_s_a22-a_0.F9_RealRMat_s_a00-a_0.F9_RealRMat_s_a11)) in\nlet r_1 = (2*r_0) in\n(EqS10_RealQuat_s\n  {\n     F10_RealQuat_s_qi =\n       (a_0.F9_RealRMat_s_a01-a_0.F9_RealRMat_s_a10) div r_1 ;\n     F10_RealQuat_s_qx =\n       (a_0.F9_RealRMat_s_a02+a_0.F9_RealRMat_s_a20) div r_1 ;\n     F10_RealQuat_s_qy =\n       (a_0.F9_RealRMat_s_a12+a_0.F9_RealRMat_s_a21) div r_1 ;\n     F10_RealQuat_s_qz = 1/2*r_0\n  }\n  {\n     F10_RealQuat_s_qi = Mf32_0[(shiftfield_F4_FloatQuat_qi q_0)] ;\n     F10_RealQuat_s_qx = Mf32_0[(shiftfield_F4_FloatQuat_qx q_0)] ;\n     F10_RealQuat_s_qy = Mf32_0[(shiftfield_F4_FloatQuat_qy q_0)] ;\n     F10_RealQuat_s_qz = Mf32_0[(shiftfield_F4_FloatQuat_qz q_0)]\n  })",
                                                                    "pattern": "EqS10_RealQuat_s{RealQuat_s}{RealQuat_s}" },
                                                                    "children": 
                                                                    { "Unfold 'EqS10_RealQuat_s'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "(L_l_RMat_of_FloatRMat Mf32_0 rm_0)",
                                                                    "pattern": "L_l_RMat_of_FloatRMat$Mf32$rm" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_RMat_of_FloatRMat'": 
                                                                    [ { "header": "Split",
                                                                    "tactic": "Wp.split",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "clause-goal",
                                                                    "target": "let a_0 = (shiftfield_F6_FloatRMat_m rm_0) in\nlet r_0 =\n    (\\sqrt\n      (1+Mf32_0[(shift_float32 a_0 8)]-Mf32_0[(shift_float32 a_0 0)]-\n       Mf32_0[(shift_float32 a_0 4)])) in\nlet r_1 = (2*r_0) in\n(Mf32_0[(shiftfield_F4_FloatQuat_qz q_0)]=(1/2*r_0))\n/\\ (Mf32_0[(shiftfield_F4_FloatQuat_qi q_0)]=\n    ((Mf32_0[(shift_float32 a_0 1)]-Mf32_0[(shift_float32 a_0 3)]) div r_1))\n/\\ (Mf32_0[(shiftfield_F4_FloatQuat_qx q_0)]=\n    ((Mf32_0[(shift_float32 a_0 2)]+Mf32_0[(shift_float32 a_0 6)]) div r_1))\n/\\ (Mf32_0[(shiftfield_F4_FloatQuat_qy q_0)]=\n    ((Mf32_0[(shift_float32 a_0 5)]+Mf32_0[(shift_float32 a_0 7)]) div r_1))",
                                                                    "pattern": "&====[]*[]/[]/[]/$Mf32shiftfield_F4_FloatQuat_qz" },
                                                                    "children": 
                                                                    { "Goal 1/4": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 2.7552,
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                                                                    "steps": 357 } ],
                                                                    "Goal 2/4": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 2.3541,
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                                                                    "steps": 380 } ],
                                                                    "Goal 3/4": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 2.2624,
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                                                                    "steps": 379 } ],
                                                                    "Goal 4/4": 
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                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 2.2096,
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                                                                    "steps": 379 } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ]