Skip to Content.
Sympa Menu

coq-club - Re: [Coq-Club] Merge Sort: Sorted L -> L = sort dec L?

coq-club AT inria.fr

Subject: The Coq mailing list

List archive

Re: [Coq-Club] Merge Sort: Sorted L -> L = sort dec L?


Chronological Thread 
  • From: Suneel Sarswat <suneel.sarswat AT gmail.com>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] Merge Sort: Sorted L -> L = sort dec L?
  • Date: Tue, 30 Jan 2024 23:31:55 +0530
  • Authentication-results: mail3-smtp-sop.national.inria.fr; spf=None smtp.pra=suneel.sarswat AT gmail.com; spf=Pass smtp.mailfrom=suneel.sarswat AT gmail.com; spf=None smtp.helo=postmaster AT mail-ed1-f52.google.com
  • Ironport-data: A9a23:T4UWS62YDIXVsP4jk/bD5Ul1kn2cJEfYwER7XKvMYLTBsI5bpzwHx jNLWGGEaKvYYTT8c94nbYW/o0lXvZ+Dm99kHgpl3Hw8FHgiRejtVY3IdB+oV8+xBpSeFxw/t 512hv3odp1coqr0/0/1WlTZhSAgk/vOHNIQMcacUghpXwhoVSw9vhxqnu89k+ZAjMOwa++3k YqaT/b3Zhn9hlaYDkpOs/jf8Eo05Kyo0N8llgVWic5j7Ae2e0Y9V8p3yZGZdxPQXoRSF+imc OfPpJnRErTxon/Bovv8+lrKWhViroz6ZWBiuVIKM0SWuSWukwRpukoN2FXwXm8M49mBt4gZJ NygLvVcQy9xVkHHsLx1vxW1j0iSlECJkVPKCSHXjCCd86HJW3jsk/93CFlvBIcFw8B2EVtVq dkdMwlYO3hvh8ruqF66Yuxlh8BmIcWyeY1C4DdvyjbWCftgSpfGK0nIzYUAjXFg24YURaaYO pBxhTlHNHwsZzVUJ1EaBZZ4h+6ynWb2bxVXrVuUoew85G27IAlZj+i3boKPK4PiqcN9xniig 1OFxlTAGSoYNO229z6I/Fmuv7qa9c/8cNlPTeXnp6ACbEeo7mcUEVgdUUaxieKoj1a3HdNZM U0dvCQ0xZXe72SuR9j5GhC0+TuK40RaVN1XHOk3rgqKz8I4/jp1GEAHTm5Lcdg+7fY8WAUM1 0+zhI/MACdW5ej9pW2myp+Yqja7OC4wJGAEZDMZQQZt3zUFiNFj5v4oZoY8eJNZnuHI9SfML ydmRRXSap0WhM8Pkqi3pBXJ3mjqqZ/OQQo4oA7QWwpJDz+Vhqb0OuRECnCCsp6sybp1qHHf4 RDofODAt4gz4WmlznDlfQn0NOjBCwy5GDPdm0VzOJIq6i6g/XWuFagJv2kgeRoyaplUIWK4C KM2he+3zM8DVJdNRf8nC79d9+xzksAM6Py8Cq6NMIIQPvCdiifcoH8wNCZ8IFwBYGB3zPhnZ sbFGSpdJXkdDqtjwXK3QexbuYLHNQhvrV4/savTlkz9uZLHPCD9Ye5cbDOmMLplhIva+1692 4gEaKO3J+B3C7GWjt//qtNLcTjn7BETWfjLliCgXrTfflY7RDF8UaO5LHFIU9UNopm5X9zgp hmVMnK0AnKl7ZEeAVzSMC4xW6ClRptls3MwMAolOFviiTBpYp+i4O1bP9E7dKUuvr4rh/Nlb eg3S+PZCNR2SxPD52s8a7v5p9dcbxiFv1+FEBekRzkdRKReYTL11OXqRDayyxlWPBGL7ZM/h 5aCyjLkRYEyQlU+LcTON9Oq4VCDnVkcv+NQWUH3DMFZUxju+tIyKgjarPw+E+cTIzrtmxqY0 Ae3B08DhO/v+oUazvjAtZqmnayITdRsPxN9NHbJyJqLLg/mx3qH7a4cdfeXbBbfeXjR+q7/V d5Kzvr5DuILrGxKv6V4Dbxv66A0vPnrmJN30SVmG2ftfX2wK7Y9PESD49ZDhpdNypBdpwGyf ECFofteGLeRPfLaAEwjHxUkYsuDxMMrtGHrt9ptG3rD5Qhz4LajemdRNUPViCVicZ1EALl8y uIl4MMr+wizjyQxCem/jwdWyn+tK0IRWKB2p7AYB47W0jAQ8G9gWqCFKCHK48CoUe5uY20KO T6fgZTQi4tMnnTid2UBLlmT/O5/q6lXhjV04g4jHXqrlODBpMcL5zxK0DFuTg1q3hRNiO1yH W5wNnxKH6aF/hY2pc1PQ1GTHxplATuH8HfQ0HoMrnXSFGOzZ1zOLUo8GOeDx18Y+GRiZQpm/ KmU5WLmcDTyduTz43cWdWt6jcf8FPpd2xbnms+1O+ikRbwBfivDkKuiQUEquinXK5o9q2Ofr NY74dsqT7PwMBAhhpESCq6Y8O81Yw+FLmkTesNR1voFMk+EcQ7jxAXUDV66f/5MAPn48UWYL chKDeAXXjSc0Be+lBwqNZQuEZRVwsFwvMEjf4n1L1Eoq7Gc9zplkKzB/xjE2VMEfY9crtYfG KjwKRS5DW2itVlFkTTsre5FGFaCT/sqWQne5N2xocI1T88tkec0akwj8KqGj1PMOitdwh+kl gfiZajX8u9c9bpRj7bcSqVtOyjkKPfYdvi5zwSogtEfMfLNKZjvsi0WmHnGPiNXH6cgZNBss Yuzs/vMhUbjgJcrYTqIhavbB61t4OOsVtF2KePyFmFRxgGZaf/v4jwC2mG2EoNIm9Vj/fuaR xO0Rc+zVNwNUfJP7SdxRwkHNDhFEIXxTKPrhR3lnsS2EhJHjDD2doK2x0HmfURwV3EuOaSnL iTWpvz3xNRTjLoUNS8+H/s8XqNJeg7ya5AHKe/0myKTVFSzo1W4vbDnqxosxBfLBlSAE+f4+ Zj1fQf/RjvjpJD3yMxljKIqsi01FHpdhcwCTnAZ8fNyiBG4CzciBsYZOpMkFJpVs3LT0LfVW TLzV1YhWB7NBWl8TRbB4drdB1bVQqREP9riPTUm8n+Fcyr8VsvKHLJl8Twm+HtsPCfqyOa8M 9wF53nsJV6Lz4p0QfoIrOmO6Qu9Kig2GlpTkaw8ryDzP/raKbAD1XgkEQYUECKaSYfCk0LEI WVzTmdBKK1+pYgdDu44E0O52jlA1N8s89nsRSiKydfb/Y6cyYWsDdXhbvrr3ORrgNsifdYzq LCee4dJy2+T030X/6AuvrrFREOy5e2jRqCHEUMoeeHec2xcJIjq0wPuUBfjlP0fxTM=
  • Ironport-hdrordr: A9a23:FzK5TK7t6VIhRHjeEAPXwPHXdLJyesId70hD6qkRc20tTiX8ra qTdZsgpHrJYVoqKRMdcJW7Scq9qBDnlKKdg7NhWYtKNTOO0ACVxcNZjbcKqAeQfBEWmNQts5 uIsJITNDQzNzVHZArBjzVQ2uxP/OW6
  • Ironport-phdr: A9a23:bBJnBRQAsSJ+/XkbeBQbiaPKndpsonyVAWYlg6HPa5pwe6iut67vI FbYra00ygOTDcOAs60P0LuempujcFJDyK7CikxKSIZLWR4BhJdetC0bK+nBN3fGKuX3ZTcxB sVIWQwt1Xi6NU9IBJS2PAWK8TW94jEIBxrwKxd+KPjrFY7OlcS30P2594HObwlSizexf7B/I A+4oAnNtMQajoVvJ6IswRbVv3VEfPhbymxvKV+PhRjw4du+8oB++CpKofIh8MBAUaT+f6smS LFTESorPWMo6sD1rBfPVQSA6GcSXWUQiRpIHhPK7ArmUZfrsyv1rfRy1S+HNsDrV780WDCi7 6B2SB/0jSoMKjA0/H3LhsF2kalWpg+qqR5izI7OeIyaO/R+caHdc90URmRPQ9hfWDBaD4ymc 4cCFfAMMfpEo4T/oVYFsBuwBROrBOPq0jJGm2L23ask3Os/FQHNwREuEMgUsHTPotT6LrsSW v2ywanT0DXDae1Z1in56ITSaRAuu+uMXal+cMXL1UkiDAzFjlCKpozkOzOZzPgCs2+e7+d5U ++klmEopR1rrDe12scslpfGhpgTyl3c6yl3wIQ4KMGkRUB0f9OqH4dcuz2VOYdrXM8sTG9lt Sc0x7EaupO2fSoHxZAmyhPfZfKKb5aE7xL+WOuQITl1hnRoc6+8iRaq6UWs1PHwW82u3FtJr idJiMfAumwO2hDJ6sWLVP1w9Vq/1DaLygDT8f1ELl4ulaTGKp4gw6A/m4IPvUnFAyT4gl/5j LWMeUUh4uWo6/roYrHhppKEMo97kAD+MqA3lsOhHOs0LxECX2ab9OiizrHj8kr5QLJFjv0yj KbVqozVJcMepqKhAg9V1Jgs6wqnAju4zNgVmWMLIVFFdR6dkYTlJ1LDLOr4APuhm1islS1kx /HCPr3vGJXNKX3Dna/6fbZg7U5T1hQ8zdRF65JPEL4BOunzW0Hru9zEFRI5PAm0zPzmCNV5z I8RRWWPAqqBPKPUqlCH/vgvLPWUZI8JpDb9LOAo6+P2gX8jhVAdZbWp3YcQaH2gAvtmJFyZb WPwjdcFDGcFpREzTPfqiV2HST5cfWy+X6M65jEhCYKpF53PRo63gO/J4CDuFZpPI2tCF1qkE HHydozCVe1fRjiVJ5pajzoJWLzpcIY7zg6nqEeu0KdhI+fQvDYRr4n83cRd6OjalBV0/jtxW ZfOm1qRRn15yztbDwQ927py9BQVIjar1KF5h6cdDtlP/7ZSVR98M5fAzut8AtS0WwTbf97PR kz1Cs6+D2QXSdQ8i8QLf147A8+r2wve2SenB/kOnqaQG5Uo2q3Z1nn1Yc16ziWOz7Ev2mEvW dAHLmi6nuh6/gnXCZTOlhCCiqCneKBaxyfX73iK0UKBuUhZVEh7VqCWFWsHaB7wqtL0rljHU 6foCbkjNV5ZztWeL6JRdtDzpVBPRfOmNdiHJmzswSG/AhGHwr7KZ43vE4kE9APaDkVM0wUa/ HLdcBM7Gj/kuGXGSjpnCVPoZUrot+h4snKyCEEunUmMaAV62ry59wRw57TUQu4P3r8CpCYqq illVFe70dXMDtOcpg1nNKxCaNI56V1D2CrXrQt4dpCnKqljgBYZfWEV9wv1yhN6B4EGisEwt 2wj0CJ9LKuZ1BVKcDbZlZH8N7vLK3XjqQi1Yv2zuBmW29KX96ETrfUg/g+77Uf5Swx4qyUhj oMGthnUro/HBwcTT5/rB0M+9hwh4qrffjF4/ITMk3tlLaiztDbGndMvHuosjBi6LLI9eOuJE hH/F8oCCo2gMusvzhKycxQJMeQU76cuJNyva9OJ3aeqOKBrmzfs3gElqMhtl1mB8SZxULuCx IsDzvycmBCOTSzjhUuJvcX+mIQCbjYXVDnaq2CsFMtaYat8epwOAGGlLpisx9lwsJXqXmZR6 F+pA15uNNaBQROJdBS92ARR0R9Sunm7gW6jyCQylTg1r62Z1SiIwuL4dRNBNHQZDGVliF7tJ 8CzgbV4FACzcg4kmR/j/k/g3LdSuIxwKmDSRQFDeC2+I2x5U6S2v6aPeIYVsMJu4XgRCrzsJ w3AArfmxnlSmzvuBW5f2Cw2e3mxt5P1kgY7wGORIXBvrWbILMR5xBPR/tvZFrZa2jsLQjU9i CGCXADteYn0u4/Mx9Ge6LPbNSrpTJBYfCj1wJnVsSK64TYvGhijh7WoncWhFwEm0Cj93t0sV CPSrR+6bJO4ssbyee9hYERsA0fxrsRgHYQr2JAtgpwd3T4Bj4+O4nMbuWj2ONRfn6n5aTBeI FxDi86Q+wXj1EB5eziS2oT0W3Hb2cJ7fMazfksZ3ys864ZBD6Lev9km1WNl51G/qwzWe/10m DwQnOAv5HAtiOYMoAMxzy+ZD+NaDQxCMCfrjRjN88GmofAdejO0abbpnhkb/5jpHPSYrwpbQ nq8ZpoyAXo68JBkKFyVmHzrttO/JZ+JPIpV7EHL1U+H1bQdKYptxKRWw3A8YiSk4yVjk6li3 HkMldm7pNTVdTsrpfrjREYebnqvP4sS4m2/0/gYxJrHmdD3WM0mQG1DXYO0H63yVmtO8622b UDWV2RszxXTUbvHQV3AtAE/9S+JS9bzcCjJbHgBkYc7HEnbfRMAxlBSBHJgx9Y4Dlz4nZO6N h4ounZJoAa/80UpqKogNgGjAD2H9UH4N3FtEsjZdF0PsUlD/xuHa5XAqL8jWXgJpNv561XcY m2DO1YSVD9PABfVQQu5eOHpvIilkaDQEOO6K7Gmjaymj+tYWr/IwJuu1tAj5DOQLoCUOWEkC fQn201FVHQ/GsLDmjxJRTZF3yTKJ9WWohux4EgV5oi27ejrVQTz5ICOF6oaMNNh/AqziLuCM OjYjThwKDJR3JcBjXHSz71X0FkXgiBoPz6jdNZI/TbKV77Vk7RLAgQzbipyMI5F4/t50FQXf 8Hcjdzx2/hzift0Q1ZJWFr9m924MMwHJ2buUTGPTE2PNbmAOXjK25StOfL6GeAW1r0E8UDq6 lP5Wwf5Mz+OlifkTUWqOOBI12SAOQBG/Zq6alBrAHTiS9Tvblu6NsV2hHs42+5R5DuCOGgCP Dx7a04IoKeX6HYSmeh5FmFFqGFsN/Kbkjqx4OzRK5JQuvxuSHcR9aoS8DEhxr1Z4TsRDuRyg zfXp8VyrkuOl+COzn9qXEMLpGsRwo2MukpmNOPS8ZwKChOmtFodqG6XDRoNvd5sDNbi7rtRx tb4n6X2MD5e8tjQ8KP06ODbLcuGNDwqNh+7QVY87SMARD+vcGzT3glTzavU+XqSoZw37JPrn chWIle+fFMwH/IeTE9iGY5aSKo=
  • Ironport-sdr: 65b9399f_tuNbfC+dPy7fA4Xk2R28x8V65A5JgE/DFIclD0riCORnV1Y daS/wEfSfGWOI9ipv+T+zbkhz1Gu8vQbgEG49Zw==

Thanks Dominique,
I still need to prove it? Is there any lemma that just allows me to rewrite (sort L) with L if L is Sorted?
Thanks,
Suneel

On Tue, Jan 30, 2024 at 7:15 PM Dominique Larchey-Wendling <dominique.larchey-wendling AT loria.fr> wrote:
Dear Suneel,

The spec of MergeSort should be enough:
if two lists are sorted and *permutable*, then they are equal.

Best,

Dominique


De: "Suneel Sarswat" <suneel.sarswat AT gmail.com>
À: "coq-club" <coq-club AT inria.fr>
Envoyé: Mardi 30 Janvier 2024 14:08:27
Objet: [Coq-Club] Merge Sort: Sorted L -> L = sort dec L?
Dear Members,

I have list L of unique records type.
I have defined ordertype "dec" on these records. I am using MergeSort module from standard library. Now I need to prove a basic result on this list. Any help would be appreciated.

Lemma sort_sorted L:
Sorted dec L -> L = sort dec L.

Thanks,
Suneel




Archive powered by MHonArc 2.6.19+.

Top of Page