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| Mirrors > Home > MPE Home > Th. List > splval | Structured version Visualization version Unicode version | ||
| Description: Value of the substring replacement operator. (Contributed by Stefan O'Rear, 15-Aug-2015.) |
| Ref | Expression |
|---|---|
| splval |
     ![/\](wedge.gif "/\"){kind=small} 
 
 
   splice     substr  ++ ++ substr   |
are mutually distinct and distinct from all other
variables.| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-splice 13304 |
. . 3
splice   substr
 ++  ++ substr | |
| 2 | 1 | a1i 11 |
. 2
splice substr
++ ++ substr |
| 3 | simprl 794 |
. . . . 5
| |
| 4 | fveq2 6191 |
. . . . . . . . 9
| |
| 5 | 4 | fveq2d 6195 |
. . . . . . . 8
|
| 6 | 5 | adantl 482 |
. . . . . . 7
|
| 7 | ot1stg 7182 |
. . . . . . . 8
| |
| 8 | 7 | adantl 482 |
. . . . . . 7
|
| 9 | 6, 8 | sylan9eqr 2678 |
. . . . . 6
|
| 10 | 9 | opeq2d 4409 |
. . . . 5
|
| 11 | 3, 10 | oveq12d 6668 |
. . . 4
substr substr |
| 12 | fveq2 6191 |
. . . . . 6
| |
| 13 | 12 | adantl 482 |
. . . . 5
|
| 14 | ot3rdg 7184 |
. . . . . . 7
| |
| 15 | 14 | 3ad2ant3 1084 |
. . . . . 6
|
| 16 | 15 | adantl 482 |
. . . . 5
|
| 17 | 13, 16 | sylan9eqr 2678 |
. . . 4
|
| 18 | 11, 17 | oveq12d 6668 |
. . 3
substr ++ substr ++ |
| 19 | 4 | fveq2d 6195 |
. . . . . . 7
|
| 20 | 19 | adantl 482 |
. . . . . 6
|
| 21 | ot2ndg 7183 |
. . . . . . 7
| |
| 22 | 21 | adantl 482 |
. . . . . 6
|
| 23 | 20, 22 | sylan9eqr 2678 |
. . . . 5
|
| 24 | 3 | fveq2d 6195 |
. . . . 5
|
| 25 | 23, 24 | opeq12d 4410 |
. . . 4
|
| 26 | 3, 25 | oveq12d 6668 |
. . 3
substr substr |
| 27 | 18, 26 | oveq12d 6668 |
. 2
substr
++
++ substr substr ++ ++ substr |
| 28 | elex 3212 |
. . 3
| |
| 29 | 28 | adantr 481 |
. 2
|
| 30 | otex 4933 |
. . 3
| |
| 31 | 30 | a1i 11 |
. 2
|
| 32 | ovexd 6680 |
. 2
substr ++ ++ substr | |
| 33 | 2, 27, 29, 31, 32 | ovmpt2d 6788 |
1
splice substr ++ ++ substr |
| Colors of variables: wff setvar class |
| Syntax hints: wi 4
wa 384
w3a 1037
wceq 1483
wcel 1990
cvv 3200
cop 4183
cotp 4185
cfv 5888
(class class class)co 6650 cmpt2 6652 c1st 7166 c2nd 7167 cc0 9936 chash 13117 ++ cconcat 13293 substr csubstr 13295 splice csplice 13296 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
| This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-ot 4186 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-splice 13304 |
| This theorem is referenced by: splid 13504 spllen 13505 splfv1 13506 splfv2a 13507 splval2 13508 gsumspl 17381 efgredleme 18156 efgredlemc 18158 efgcpbllemb 18168 frgpuplem 18185 splvalpfx 41435 |
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