lemma_anticomm_cross_product.json 7.43 KB
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[ { "header": "Definition", "tactic": "Wp.unfold", "params": {},
    "select": { "select": "inside-goal", "occur": 0,
                "target": "(L_cross_product v2_0 v1_0)",
                "pattern": "L_cross_product$v2$v1" },
    "children": { "Unfold 'L_cross_product'": [ { "header": "Definition",
                                                  "tactic": "Wp.unfold",
                                                  "params": {},
                                                  "select": { "select": "inside-goal",
                                                              "occur": 0,
                                                              "target": "let r_0 = v1_0.F12_RealVect3_s_y in\nlet r_1 = v2_0.F12_RealVect3_s_z in\nlet r_2 = v1_0.F12_RealVect3_s_z in\nlet r_3 = v2_0.F12_RealVect3_s_y in\nlet r_4 = v2_0.F12_RealVect3_s_x in\nlet r_5 = v1_0.F12_RealVect3_s_x in\n(L_mult_scalar_1_ -1\n  {\n     F12_RealVect3_s_x = (r_2*r_3)-(r_0*r_1) ;\n     F12_RealVect3_s_y = (r_5*r_1)-(r_2*r_4) ;\n     F12_RealVect3_s_z = (r_0*r_4)-(r_5*r_3)\n  })",
                                                              "pattern": "L_mult_scalar_1_-1{RealVect3_s}+" },
                                                  "children": { "Unfold 'L_mult_scalar_1_'": 
                                                                  [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "inside-goal",
                                                                    "occur": 0,
                                                                    "target": "(L_cross_product v1_0 v2_0)",
                                                                    "pattern": "L_cross_product$v1$v2" },
                                                                    "children": 
                                                                    { "Unfold 'L_cross_product'": 
                                                                    [ { "header": "Definition",
                                                                    "tactic": "Wp.unfold",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "clause-goal",
                                                                    "target": "let r_0 = v1_0.F12_RealVect3_s_z in\nlet r_1 = v2_0.F12_RealVect3_s_y in\nlet r_2 = (r_0*r_1) in\nlet r_3 = v1_0.F12_RealVect3_s_y in\nlet r_4 = v2_0.F12_RealVect3_s_z in\nlet r_5 = (r_3*r_4) in\nlet r_6 = v1_0.F12_RealVect3_s_x in\nlet r_7 = (r_6*r_4) in\nlet r_8 = v2_0.F12_RealVect3_s_x in\nlet r_9 = (r_0*r_8) in\nlet r_10 = (r_3*r_8) in\nlet r_11 = (r_6*r_1) in\n(EqS12_RealVect3_s\n  {\n     F12_RealVect3_s_x = r_5-r_2 ;\n     F12_RealVect3_s_y = r_9-r_7 ;\n     F12_RealVect3_s_z = r_11-r_10\n  }\n  {\n     F12_RealVect3_s_x = -1*(r_2-r_5) ;\n     F12_RealVect3_s_y = -1*(r_7-r_9) ;\n     F12_RealVect3_s_z = -1*(r_10-r_11)\n  })",
                                                                    "pattern": "EqS12_RealVect3_s{RealVect3_s}{RealVect3_s}" },
                                                                    "children": 
                                                                    { "Unfold 'EqS12_RealVect3_s'": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
                                                                    "time": 0.0181,
                                                                    "steps": 8 },
                                                                    { "header": "Split",
                                                                    "tactic": "Wp.split",
                                                                    "params": {},
                                                                    "select": 
                                                                    { "select": "clause-goal",
                                                                    "target": "let r_0 = v1_0.F12_RealVect3_s_x in\nlet r_1 = v2_0.F12_RealVect3_s_x in\nlet r_2 = (r_0*r_1) in\nlet r_3 = v1_0.F12_RealVect3_s_y in\nlet r_4 = v2_0.F12_RealVect3_s_y in\nlet r_5 = (r_3*r_4) in\nlet r_6 = v2_0.F12_RealVect3_s_z in\nlet r_7 = (r_3*r_6) in\nlet r_8 = v1_0.F12_RealVect3_s_z in\nlet r_9 = (r_8*r_4) in\nlet r_10 = (r_8*r_1) in\nlet r_11 = (r_0*r_6) in\n(r_2=(r_5+(-1*(r_2-r_5)))) /\\ (r_7=(r_9+(-1*(r_9-r_7))))\n/\\ (r_10=(r_11+(-1*(r_11-r_10))))",
                                                                    "pattern": "&===*+*+*+.F12_RealVect3_s_x.F12_RealVect3_s_x" },
                                                                    "children": 
                                                                    { "Goal 1/3": 
                                                                    [ { "prover": "Z3:4.8.6:noBV",
                                                                    "verdict": "timeout",
                                                                    "time": 10. },
                                                                    { "prover": "Z3:4.8.6:counterexamples",
                                                                    "verdict": "unknown" },
                                                                    { "prover": "Z3:4.8.6",
                                                                    "verdict": "timeout",
                                                                    "time": 10. },
                                                                    { "prover": "Coq:8.12.2",
                                                                    "verdict": "unknown" },
                                                                    { "prover": "CVC4:1.9-prerelease:strings+counterexamples",
                                                                    "verdict": "unknown" },
                                                                    { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "timeout",
                                                                    "time": 10. } ],
                                                                    "Goal 2/3": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
                                                                    "time": 0.0062,
                                                                    "steps": 8 } ],
                                                                    "Goal 3/3": 
                                                                    [ { "prover": "Alt-Ergo:2.3.3",
                                                                    "verdict": "valid",
                                                                    "time": 0.0109,
                                                                    "steps": 8 } ] } } ] } } ] } } ] } } ] } } ]