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Mirrors > Home > ILE Home > Th. List > flval | Unicode version |
Description: Value of the floor (greatest integer) function. The floor of is the (unique) integer less than or equal to whose successor is strictly greater than . (Contributed by NM, 14-Nov-2004.) (Revised by Mario Carneiro, 2-Nov-2013.) |
Ref | Expression |
---|---|
flval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 3789 | . . . 4 | |
2 | breq1 3788 | . . . 4 | |
3 | 1, 2 | anbi12d 456 | . . 3 |
4 | 3 | riotabidv 5490 | . 2 |
5 | df-fl 9274 | . 2 | |
6 | zex 8360 | . . 3 | |
7 | riotaexg 5492 | . . 3 | |
8 | 6, 7 | ax-mp 7 | . 2 |
9 | 4, 5, 8 | fvmpt3i 5273 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 cvv 2601 class class class wbr 3785 cfv 4922 crio 5487 (class class class)co 5532 cr 6980 c1 6982 caddc 6984 clt 7153 cle 7154 cz 8351 cfl 9272 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-cnex 7067 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-iota 4887 df-fun 4924 df-fv 4930 df-riota 5488 df-ov 5535 df-neg 7282 df-z 8352 df-fl 9274 |
This theorem is referenced by: flqcl 9277 flqlelt 9278 flqbi 9292 |
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