DemoChecker Proof

Automatic Checking

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{ "type": "solutionelement", "name": "solutionelement-checkerdemo", "metadata": {}, "data": { "contents": [{"id": "sdelement-demodata"}], "contentdata": { "sdelement-demodata": { "type": "sdelement", "name": "sdelement-demodata", "metadata": {}, "data": { "dstepdata": { "declaration-ralph.back-20190425125838404-296": { "label": "+", "text": "", "readonly": false, "fillable": false, "attrs": {}, "type": "declaration", "definition": { "text": "$a_1{,}a_2\\in\\RR$", "readonly": false, "fillable": false, "istext": true, "attrs": {} } }, "stask-ralph.back-20190425125630512-692": { "readonly": false, "task": [ { "text": "Prove that $2a_1a_2\\le a_1^2+a_2^2$", "type": "prove", "readonly": false, "fillable": false, "attrs": {}, "answer": { "text": "", "readonly": false, "fillable": false, "attrs": {} } } ], "assumption": [], "observation": [], "derivmotivation": [], "term": [ { "text": "2a_1a_2\\le a_1^2+a_2^2", "readonly": false, "fillable": false, "attrs": {} }, { "text": "0\\le a_1^2+a_2^2-2a_1a_2", "readonly": false, "fillable": false, "attrs": {} }, { "text": "0\\le\\left(a_1-a_2\\right)^2", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\T", "readonly": false, "fillable": false, "attrs": {} } ], "relation": [ { "text": "\\Leftrightarrow", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\Leftrightarrow", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\Leftrightarrow", "readonly": false, "fillable": false, "attrs": {} } ], "motivation": [ { "text": "add $-2a_1a_2$ to both sides, simplify", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} }, { "text": "binomial expression", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} }, { "text": "a square is always nonnegative", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} } ] } }, "caption": { "text": "Example solution:", "readonly": true, "fillable": false, "attrs": {} }, "dsteps": [ { "id": "declaration-ralph.back-20190425125838404-296", "type": "observation" }, { "id": "stask-ralph.back-20190425125630512-692", "type": "task" } ] } } } } }

Proofs

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Use the checker always when practicing math