float_quat_of_rmat_a11_max_ensures.json 9.6 KB
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[ { "header": "Definition", "tactic": "Wp.unfold", "params": {},
    "select": { "select": "inside-goal", "occur": 0,
                "target": "(L_l_FloatQuat_of_RMat_1_max_t Mf32_0 rm_0)",
                "pattern": "L_l_FloatQuat_of_RMat_1_max_t$Mf32" },
    "children": { "Unfold 'L_l_FloatQuat_of_RMat_1_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-goal",
                                                                    "occur": 0,
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                                                                    "target": "let a_0 = (L_l_RMat_of_FloatRMat Mf32_0 rm_0) in\n(L_l_FloatQuat_of_RMat_1_max_1_\n  {\n     a_0 with\n     F12_RealRMat_s_a01 = a_0.F12_RealRMat_s_a10 ;\n     F12_RealRMat_s_a02 = a_0.F12_RealRMat_s_a20 ;\n     F12_RealRMat_s_a10 = a_0.F12_RealRMat_s_a01 ;\n     F12_RealRMat_s_a12 = a_0.F12_RealRMat_s_a21 ;\n     F12_RealRMat_s_a20 = a_0.F12_RealRMat_s_a02 ;\n     F12_RealRMat_s_a21 = a_0.F12_RealRMat_s_a12\n  })",
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                                                                    "pattern": "L_l_FloatQuat_of_RMat_1_max_1_{RealRMat_s}" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_FloatQuat_of_RMat_1_max_1_'": 
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                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 8.7286,
                                                                    "steps": 1690 },
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                                                                    { "header": "Definition",
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                                                                    "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_a11-a_0.F9_RealRMat_s_a00-a_0.F9_RealRMat_s_a22)) in\nlet r_1 = (2*r_0) in\n(EqS10_RealQuat_s\n  {\n     F10_RealQuat_s_qi =\n       (a_0.F9_RealRMat_s_a20-a_0.F9_RealRMat_s_a02) div r_1 ;\n     F10_RealQuat_s_qx =\n       (a_0.F9_RealRMat_s_a01+a_0.F9_RealRMat_s_a10) div r_1 ;\n     F10_RealQuat_s_qy = 1/2*r_0 ;\n     F10_RealQuat_s_qz =\n       (a_0.F9_RealRMat_s_a12+a_0.F9_RealRMat_s_a21) div r_1\n  } (L_l_Quat_of_FloatQuat Mf32_0 q_0))",
                                                                    "pattern": "EqS10_RealQuat_s{RealQuat_s}L_l_Quat_of_FloatQuat" },
                                                                    "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$rm" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_RMat_of_FloatRMat'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "(L_l_Quat_of_FloatQuat Mf32_0 q_0)",
                                                                    "pattern": "L_l_Quat_of_FloatQuat$Mf32$q" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_Quat_of_FloatQuat'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-step",
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                                                                    "at": 3,
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                                                                    "kind": "have",
                                                                    "occur": 0,
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                                                                    "target": "(L_trace_2_ Mf32_27 rm_0)",
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                                                                    "pattern": "L_trace_2_$Mf32$rm" },
                                                                    "children": 
                                                                    { "Unfold 'L_trace_2_'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-step",
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                                                                    "at": 3,
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                                                                    "kind": "have",
                                                                    "occur": 0,
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                                                                    "target": "(L_trace_1_ (L_l_RMat_of_FloatRMat Mf32_27 rm_0))",
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                                                                    "pattern": "L_trace_1_L_l_RMat_of_FloatRMat$Mf32" },
                                                                    "children": 
                                                                    { "Unfold 'L_trace_1_'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-step",
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                                                                    "at": 3,
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                                                                    "kind": "have",
                                                                    "occur": 0,
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                                                                    "target": "(L_l_RMat_of_FloatRMat Mf32_27 rm_0)",
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                                                                    "pattern": "L_l_RMat_of_FloatRMat$Mf32$rm" },
                                                                    "children": 
                                                                    { "Unfold 'L_l_RMat_of_FloatRMat'": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
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                                                                    "time": 3.9911,
                                                                    "steps": 1765 } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ] } } ]