metamath/valid/algebra-sqineq-4bap1lt4bsqpap1sq.mm (34 lines of code) (raw):

${ algebra-sqineq-4bap1lt4bsqpap1sq.0 $e |- ( ph -> A e. RR ) $. algebra-sqineq-4bap1lt4bsqpap1sq.1 $e |- ( ph -> B e. RR ) $. $( (Contributed by Stanislas Polu, 26-Nov-2020.) $) algebra-sqineq-4bap1lt4bsqpap1sq $p |- ( ph -> ( ( 4 x. B ) x. ( A + 1 ) ) <_ ( ( 4 x. ( B ^ 2 ) ) + ( ( A + 1 ) ^ 2 ) ) ) $= ( c4 cmul co c1 caddc cexp cle cc0 cmin mulcld breqtrd eqcomd eqtrd oveq2d c2 wbr cr wcel 2re a1i remulcld 1red resubcld sqge0d wceq 2cnd recnd subcld cc binom2sub syl2anc mulassd mul32d oveq1d subadd23d subdid subsub2d sqmuld sqcld sq2 mulid1d 2t2e4 oveq12d 4re resqcld addsubd addsubassd addcld mul4d mulcomd eqtr2d subsub4d addcomd add12d binom2 adddid readdcld bicomd mpbird 1cnd subge0d ) AFCGHZBIJHZGHZFCTKHZGHZWHTKHZJHZLUAZMWMWINHZLUAZAMWKBTKHZTBI GHZGHZJHZITKHZJHZJHZWGBGHZWGIGHZJHZNHZWOLAMWKXAJHZWTJHZXDWGJHZNHZXGLAMXIWGX DJHZNHZXKLAMXIWGNHZXDNHZXMLAMXHWGNHZWQTBGHZIGHZJHZJHZXQTCGHZGHZNHZXOLAMXPXS YBNHZJHZYCLAMYAINHZTKHZWQXRYBNHJHZJHZYELAMYGWQYBXRNHZNHZJHZYILAMYGWQXQYFGHZ NHZJHZYLLAMYGYMNHZWQJHZYOLAMYGTYFBGHGHZNHZWQJHZYQLAMYFBNHZTKHZYTLAUUAAYFBAY AIATCTUBUCAUDUEEUFAUGZUHDUHUIAYFUNUCBUNUCZUUBYTUJAYAIATCAUKZACEULZOZAWEZUMZ ABDULZYFBUOUPPAYSYPWQJAYRYMYGNAYRTYFGHBGHZYMAUUKYRATYFBUUEUUIUUJUQQATYFBUUE UUIUUJURRSUSPAYGYMWQAYFUUIVDAXQYFATBUUEUUJOZUUIOABUUJVDZUTPAYNYKYGJAYMYJWQN AXQYAIUULUUGUUHVASSPAYKYHYGJAWQYBXRUUMAXQYAUULUUGOZAXQIUULUUHOZVBSPAYGXPYHY DJAYGWKWGNHZXAJHZXPAYGYATKHZTYAIGHZGHZNHZXAJHZUUQAYAUNUCIUNUCZYGUVBUJUUGUUH YAIUOUPAUVAUUPXAJAUURWKUUTWGNAUURTTKHZWJGHWKATCUUEUUFVCAUVDFWJGUVDFUJAVEUEU SRAUUTTYAGHZWGAUUSYATGAYAUUGVFSAWGUVEAWGTTGHZCGHUVEAFUVFCGAUVFFUVFFUJAVGUEZ QUSATTCUUEUUEUUFUQRQRVHUSRAXPUUQAWKXAWGAWKAFWJFUBUCAVIUEZACEVJUFZULZAIUUHVD ZAFCAFUVHULZUUFOZVKQRAYDYHAWQXRYBUUMUUOUUNVLQVHPAYCYEAXPXSYBAXHWGAWKXAUVJUV KVMZUVMUMAWQXRUUMUUOVMUUNVLQPAXTXNYBXDNAXNXTAXNXPWTJHXTAXHWTWGUVNAWQWSUUMAT WRUUEABIUUJUUHOOVMZUVMVKAWTXSXPJAWSXRWQJAXRWSATBIUUEUUJUUHUQQSSRQAYBFBCGHZG HZXDAYBUVFUVPGHUVQATBTCUUEUUJUUEUUFVNAUVFFUVPGUVGUSRAXDFCBGHZGHUVQAFCBUVLUU FUUJUQAUVRUVPFGACBUUFUUJVOSVPRVHPAXIWGXDAXHWTUVNUVOVMUVMAWGBUVMUUJOZVQPAXLX JXINAWGXDUVMUVSVRSPAXIXCXJXFNAXIWTXHJHXCAXHWTUVNUVOVRAWTWKXAUVOUVJUVKVSRAWG XEXDJAXEWGAWGUVMVFQSVHPAXCWMXFWINAXBWLWKJAWLXBAUUDUVCWLXBUJUUJUUHBIVTUPQSAW IXFAWGBIUVMUUJUUHWAQVHPAWPWNAWMWIAWKWLUVIAWHABIDUUCWBZVJWBAWGWHAFCUVHEUFUVT UFWFWCWD $. $}