↑

scratchproof in Scrabble®

The word scratchproof is playable in Scrabble®, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.

Scrabble® Letter Score: 24

Highest Scoring Scrabble® Play In The Letters scratchproof:

SCRATCHPROOF
(261)

Seven Letter Word Alert: (21 words)

cahoots, captors, carhops, carport, carrots, coactor, coarcts, cohorts, corpora, factors, octarch, orators, parrots, proctor, raptors, scratch, scrooch, toparch, torpors, trocars, trochar

 

All Scrabble® Plays For The Word scratchproof

SCRATCHPROOF
(261)
SCRATCHPROOF
(234)
SCRATCHPROOF
(174)
SCRATCHPROOF
(156)
SCRATCHPROOF
(120)
SCRATCHPROOF
(116)
SCRATCHPROOF
(116)
SCRATCHPROOF
(112)
SCRATCHPROOF
(112)
SCRATCHPROOF
(108)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
SCRATCHPROOF
(84)
SCRATCHPROOF
(78)
SCRATCHPROOF
(68)
SCRATCHPROOF
(64)
SCRATCHPROOF
(64)
SCRATCHPROOF
(58)
SCRATCHPROOF
(56)
SCRATCHPROOF
(56)
SCRATCHPROOF
(56)
SCRATCHPROOF
(52)
SCRATCHPROOF
(40)
SCRATCHPROOF
(38)
SCRATCHPROOF
(37)
SCRATCHPROOF
(36)
SCRATCHPROOF
(31)
SCRATCHPROOF
(30)
SCRATCHPROOF
(30)
SCRATCHPROOF
(29)

The 200 Highest Scoring Scrabble® Plays For Words Using The Letters In scratchproof

SCRATCHPROOF
(261)
SCRATCHPROOF
(234)
SCRATCHPROOF
(174)
SCRATCHPROOF
(156)
SCRATCHPROOF
(120)
SCRATCHPROOF
(116)
SCRATCHPROOF
(116)
SCRATCHPROOF
(112)
SCRATCHPROOF
(112)
SCRATCHPROOF
(108)
SCRATCH
(106 = 56 + 50)
OCTARCH
(106 = 56 + 50)
SCROOCH
(106 = 56 + 50)
CARHOPS
(106 = 56 + 50)
TOPARCH
(106 = 56 + 50)
TOPARCH
(104 = 54 + 50)
SCRATCH
(104 = 54 + 50)
CARHOPS
(104 = 54 + 50)
SCROOCH
(104 = 54 + 50)
CARHOPS
(104 = 54 + 50)
OCTARCH
(104 = 54 + 50)
SCRATCH
(101 = 51 + 50)
CARHOPS
(101 = 51 + 50)
SCRATCH
(101 = 51 + 50)
CARHOPS
(101 = 51 + 50)
OCTARCH
(101 = 51 + 50)
SCROOCH
(101 = 51 + 50)
SCROOCH
(101 = 51 + 50)
OCTARCH
(101 = 51 + 50)
TOPARCH
(101 = 51 + 50)
TOPARCH
(101 = 51 + 50)
COHORTS
(98 = 48 + 50)
FACTORS
(98 = 48 + 50)
TROCHAR
(98 = 48 + 50)
TROCHAR
(98 = 48 + 50)
CAHOOTS
(98 = 48 + 50)
FACTORS
(98 = 48 + 50)
COHORTS
(98 = 48 + 50)
CAHOOTS
(98 = 48 + 50)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
SCRATCHPROOF
(96)
OCTARCH
(95 = 45 + 50)
OCTARCH
(95 = 45 + 50)
OCTARCH
(95 = 45 + 50)
SCRATCH
(95 = 45 + 50)
CARHOPS
(95 = 45 + 50)
CARHOPS
(95 = 45 + 50)
COHORTS
(95 = 45 + 50)
CARHOPS
(95 = 45 + 50)
CARHOPS
(95 = 45 + 50)
TROCHAR
(95 = 45 + 50)
OCTARCH
(95 = 45 + 50)
FACTORS
(95 = 45 + 50)
TROCHAR
(95 = 45 + 50)
SCRATCH
(95 = 45 + 50)
OCTARCH
(95 = 45 + 50)
SCROOCH
(95 = 45 + 50)
SCROOCH
(95 = 45 + 50)
SCROOCH
(95 = 45 + 50)
SCRATCH
(95 = 45 + 50)
SCRATCH
(95 = 45 + 50)
CAHOOTS
(95 = 45 + 50)
SCROOCH
(95 = 45 + 50)
TOPARCH
(95 = 45 + 50)
SCRATCH
(95 = 45 + 50)
TOPARCH
(95 = 45 + 50)
TOPARCH
(95 = 45 + 50)
TOPARCH
(95 = 45 + 50)
TOPARCH
(95 = 45 + 50)
SCROOCH
(95 = 45 + 50)
PROCTOR
(94 = 44 + 50)
CORPORA
(94 = 44 + 50)
CARPORT
(94 = 44 + 50)
CAPTORS
(94 = 44 + 50)
COACTOR
(94 = 44 + 50)
COARCTS
(94 = 44 + 50)
CARPORT
(92 = 42 + 50)
OCTARCH
(92 = 42 + 50)
PROCTOR
(92 = 42 + 50)
PROCTOR
(92 = 42 + 50)
SCRATCH
(92 = 42 + 50)
CORPORA
(92 = 42 + 50)
SCROOCH
(92 = 42 + 50)
COACTOR
(92 = 42 + 50)
CAPTORS
(92 = 42 + 50)
CAPTORS
(92 = 42 + 50)
CARHOPS
(92 = 42 + 50)
PROCTOR
(92 = 42 + 50)
CORPORA
(92 = 42 + 50)
TOPARCH
(92 = 42 + 50)
CORPORA
(92 = 42 + 50)
CARPORT
(92 = 42 + 50)
COARCTS
(92 = 42 + 50)
COACTOR
(92 = 42 + 50)
COARCTS
(92 = 42 + 50)
CARPORT
(92 = 42 + 50)
COACTOR
(92 = 42 + 50)
SCRATCH
(90 = 40 + 50)
CAHOOTS
(90 = 40 + 50)
TOPARCH
(90 = 40 + 50)
SCROOCH
(90 = 40 + 50)
SCROOCH
(90 = 40 + 50)
TOPARCH
(90 = 40 + 50)
OCTARCH
(90 = 40 + 50)
OCTARCH
(90 = 40 + 50)
TROCHAR
(90 = 40 + 50)
SCRATCH
(90 = 40 + 50)
CARHOPS
(90 = 40 + 50)
COHORTS
(90 = 40 + 50)
COHORTS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
COHORTS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
TROCHAR
(89 = 39 + 50)
COHORTS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
COHORTS
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
COHORTS
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
COHORTS
(89 = 39 + 50)
TROCHAR
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
TROCHAR
(89 = 39 + 50)
FACTORS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
CAHOOTS
(89 = 39 + 50)
TROCHAR
(89 = 39 + 50)
TROCHAR
(89 = 39 + 50)
SCRATCH
(88 = 38 + 50)
OCTARCH
(88 = 38 + 50)
COHORTS
(88 = 38 + 50)
TOPARCH
(88 = 38 + 50)
FACTORS
(88 = 38 + 50)
SCROOCH
(88 = 38 + 50)
CAHOOTS
(88 = 38 + 50)
OCTARCH
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
CARPORT
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
SCROOCH
(86 = 36 + 50)
PARROTS
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
PROCTOR
(86 = 36 + 50)
TORPORS
(86 = 36 + 50)
CARROTS
(86 = 36 + 50)
PROCTOR
(86 = 36 + 50)
TOPARCH
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
PARROTS
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
COACTOR
(86 = 36 + 50)
COACTOR
(86 = 36 + 50)
RAPTORS
(86 = 36 + 50)
PROCTOR
(86 = 36 + 50)
COACTOR
(86 = 36 + 50)
COHORTS
(86 = 36 + 50)
CARPORT
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
TORPORS
(86 = 36 + 50)
COACTOR
(86 = 36 + 50)
CORPORA
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
TORPORS
(86 = 36 + 50)
CARHOPS
(86 = 36 + 50)
SCROOCH
(86 = 36 + 50)
SCRATCH
(86 = 36 + 50)
CARPORT
(86 = 36 + 50)
FACTORS
(86 = 36 + 50)
TROCARS
(86 = 36 + 50)
CAPTORS
(86 = 36 + 50)
TOPARCH
(86 = 36 + 50)
TROCARS
(86 = 36 + 50)
OCTARCH
(86 = 36 + 50)
CORPORA
(86 = 36 + 50)
TOPARCH
(86 = 36 + 50)
CARROTS
(86 = 36 + 50)
CAHOOTS
(86 = 36 + 50)
RAPTORS
(86 = 36 + 50)
TROCHAR
(86 = 36 + 50)
TROCARS
(86 = 36 + 50)
SCRATCH
(86 = 36 + 50)
FACTORS
(86 = 36 + 50)
CORPORA
(86 = 36 + 50)
CARPORT
(86 = 36 + 50)
COACTOR
(86 = 36 + 50)
CORPORA
(86 = 36 + 50)
PROCTOR
(86 = 36 + 50)
CORPORA
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
CARPORT
(86 = 36 + 50)
PROCTOR
(86 = 36 + 50)
COARCTS
(86 = 36 + 50)
Your Best
Scrabble
PlaysLegendary
Scrabble
Plays
↑

scratchproof in Words With Friends™

The word scratchproof is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.

Words With Friends™ Letter Score: 26

Highest Scoring Words With Friends™ Play In The Letters scratchproof:

SCRATCHPROOF
(378)

Seven Letter Word Alert: (21 words)

cahoots, captors, carhops, carport, carrots, coactor, coarcts, cohorts, corpora, factors, octarch, orators, parrots, proctor, raptors, scratch, scrooch, toparch, torpors, trocars, trochar

 

All Words With Friends™ Plays For The Word scratchproof

SCRATCHPROOF
(378)
SCRATCHPROOF
(324)
SCRATCHPROOF
(306)
SCRATCHPROOF
(306)
SCRATCHPROOF
(216)
SCRATCHPROOF
(180)
SCRATCHPROOF
(136)
SCRATCHPROOF
(112)
SCRATCHPROOF
(108)
SCRATCHPROOF
(108)
SCRATCHPROOF
(104)
SCRATCHPROOF
(104)
SCRATCHPROOF
(104)
SCRATCHPROOF
(104)
SCRATCHPROOF
(72)
SCRATCHPROOF
(72)
SCRATCHPROOF
(72)
SCRATCHPROOF
(68)
SCRATCHPROOF
(60)
SCRATCHPROOF
(60)
SCRATCHPROOF
(42)
SCRATCHPROOF
(42)
SCRATCHPROOF
(35)
SCRATCHPROOF
(32)
SCRATCHPROOF
(32)
SCRATCHPROOF
(32)
SCRATCHPROOF
(32)
SCRATCHPROOF
(31)
SCRATCHPROOF
(30)
SCRATCHPROOF
(29)
SCRATCHPROOF
(28)
SCRATCHPROOF
(28)

The 200 Highest Scoring Words With Friends™ Plays Using The Letters In scratchproof

SCRATCHPROOF
(378)
SCRATCHPROOF
(324)
SCRATCHPROOF
(306)
SCRATCHPROOF
(306)
SCRATCHPROOF
(216)
SCRATCHPROOF
(180)
SCRATCHPROOF
(136)
CAPTORS
(122 = 87 + 35)
CARHOPS
(122 = 87 + 35)
FACTORS
(122 = 87 + 35)
COHORTS
(113 = 78 + 35)
CAHOOTS
(113 = 78 + 35)
SCRATCHPROOF
(112)
SCRATCH
(110 = 75 + 35)
SCROOCH
(110 = 75 + 35)
SCROOCH
(110 = 75 + 35)
OCTARCH
(110 = 75 + 35)
OCTARCH
(110 = 75 + 35)
TOPARCH
(110 = 75 + 35)
SCRATCH
(110 = 75 + 35)
TOPARCH
(110 = 75 + 35)
CARHOPS
(110 = 75 + 35)
SCRATCHPROOF
(108)
SCRATCHPROOF
(108)
PROCTOR
(104 = 69 + 35)
CARPORT
(104 = 69 + 35)
CARHOPS
(104 = 69 + 35)
OCTARCH
(104 = 69 + 35)
CARPORT
(104 = 69 + 35)
CORPORA
(104 = 69 + 35)
CORPORA
(104 = 69 + 35)
PROCTOR
(104 = 69 + 35)
COACTOR
(104 = 69 + 35)
PROCTOR
(104 = 69 + 35)
CARPORT
(104 = 69 + 35)
CORPORA
(104 = 69 + 35)
COACTOR
(104 = 69 + 35)
COACTOR
(104 = 69 + 35)
CARHOPS
(104 = 69 + 35)
SCRATCH
(104 = 69 + 35)
SCROOCH
(104 = 69 + 35)
SCRATCHPROOF
(104)
SCRATCH
(104 = 69 + 35)
OCTARCH
(104 = 69 + 35)
SCRATCHPROOF
(104)
SCRATCH
(104 = 69 + 35)
TOPARCH
(104 = 69 + 35)
COARCTS
(104 = 69 + 35)
SCRATCHPROOF
(104)
OCTARCH
(104 = 69 + 35)
TOPARCH
(104 = 69 + 35)
SCRATCHPROOF
(104)
SCROOCH
(104 = 69 + 35)
COARCTS
(104 = 69 + 35)
CARHOPS
(104 = 69 + 35)
SCROOCH
(104 = 69 + 35)
TROCHAR
(101 = 66 + 35)
TROCHAR
(101 = 66 + 35)
PROCTOR
(98 = 63 + 35)
OCTARCH
(98 = 63 + 35)
SCRATCH
(98 = 63 + 35)
COACTOR
(98 = 63 + 35)
CARHOPS
(98 = 63 + 35)
CARPORT
(98 = 63 + 35)
COACTOR
(98 = 63 + 35)
CARPORT
(98 = 63 + 35)
CARPORT
(98 = 63 + 35)
COARCTS
(98 = 63 + 35)
CARHOPS
(98 = 63 + 35)
COACTOR
(98 = 63 + 35)
PROCTOR
(98 = 63 + 35)
CORPORA
(98 = 63 + 35)
PROCTOR
(98 = 63 + 35)
FACTORS
(98 = 63 + 35)
CAPTORS
(98 = 63 + 35)
CORPORA
(98 = 63 + 35)
SCROOCH
(98 = 63 + 35)
CORPORA
(98 = 63 + 35)
TOPARCH
(98 = 63 + 35)
TOPARCH
(95 = 60 + 35)
TROCHAR
(95 = 60 + 35)
OCTARCH
(95 = 60 + 35)
PARROTS
(95 = 60 + 35)
CAHOOTS
(95 = 60 + 35)
CARHOPS
(95 = 60 + 35)
SCROOCH
(95 = 60 + 35)
SCRATCH
(95 = 60 + 35)
CARROTS
(95 = 60 + 35)
OCTARCH
(95 = 60 + 35)
TOPARCH
(95 = 60 + 35)
SCROOCH
(95 = 60 + 35)
TOPARCH
(95 = 60 + 35)
TROCHAR
(95 = 60 + 35)
TORPORS
(95 = 60 + 35)
SCRATCH
(95 = 60 + 35)
TROCHAR
(95 = 60 + 35)
SCROOCH
(95 = 60 + 35)
TORPORS
(95 = 60 + 35)
SCRATCH
(95 = 60 + 35)
TROCARS
(95 = 60 + 35)
COHORTS
(95 = 60 + 35)
CARHOPS
(95 = 60 + 35)
OCTARCH
(95 = 60 + 35)
RAPTORS
(95 = 60 + 35)
TROCARS
(95 = 60 + 35)
CARHOPS
(95 = 60 + 35)
OCTARCH
(92 = 57 + 35)
CARHOPS
(92 = 57 + 35)
SCROOCH
(92 = 57 + 35)
TOPARCH
(92 = 57 + 35)
SCRATCH
(92 = 57 + 35)
CARROTS
(89 = 54 + 35)
TORPORS
(89 = 54 + 35)
TORPORS
(89 = 54 + 35)
TROCARS
(89 = 54 + 35)
TROCARS
(89 = 54 + 35)
PARROTS
(89 = 54 + 35)
CORPORA
(87 = 52 + 35)
FACTORS
(87 = 52 + 35)
COARCTS
(87 = 52 + 35)
COARCTS
(87 = 52 + 35)
CORPORA
(87 = 52 + 35)
COARCTS
(87 = 52 + 35)
CAPTORS
(87 = 52 + 35)
CAPTORS
(87 = 52 + 35)
CARPORT
(87 = 52 + 35)
CAPTORS
(87 = 52 + 35)
CARPORT
(87 = 52 + 35)
CARPORT
(87 = 52 + 35)
CORPORA
(87 = 52 + 35)
FACTORS
(87 = 52 + 35)
PROCTOR
(87 = 52 + 35)
COACTOR
(87 = 52 + 35)
PROCTOR
(87 = 52 + 35)
FACTORS
(87 = 52 + 35)
COACTOR
(87 = 52 + 35)
PROCTOR
(87 = 52 + 35)
COACTOR
(87 = 52 + 35)
COACTOR
(86 = 51 + 35)
PROCTOR
(86 = 51 + 35)
TOPARCH
(86 = 51 + 35)
OCTARCH
(86 = 51 + 35)
COARCTS
(86 = 51 + 35)
SCROOCH
(86 = 51 + 35)
SCROOCH
(86 = 51 + 35)
OCTARCH
(86 = 51 + 35)
CARPORT
(86 = 51 + 35)
SCRATCH
(86 = 51 + 35)
TOPARCH
(86 = 51 + 35)
SCROOCH
(86 = 51 + 35)
CARHOPS
(86 = 51 + 35)
TOPARCH
(86 = 51 + 35)
FACTORS
(86 = 51 + 35)
TOPARCH
(86 = 51 + 35)
SCRATCH
(86 = 51 + 35)
CARHOPS
(86 = 51 + 35)
OCTARCH
(86 = 51 + 35)
FACTORS
(86 = 51 + 35)
FACTORS
(86 = 51 + 35)
COARCTS
(86 = 51 + 35)
CAPTORS
(86 = 51 + 35)
CAPTORS
(86 = 51 + 35)
CAPTORS
(86 = 51 + 35)
CORPORA
(86 = 51 + 35)
SCRATCH
(86 = 51 + 35)
CAPTOR
(84)
CARHOP
(84)
FACTOR
(84)
COCOAS
(84)
CAHOOTS
(83 = 48 + 35)
CAHOOTS
(83 = 48 + 35)
TROCHAR
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
TROCHAR
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
TROCHAR
(83 = 48 + 35)
TROCHAR
(83 = 48 + 35)
CAHOOTS
(83 = 48 + 35)
CAHOOTS
(83 = 48 + 35)
CAHOOTS
(83 = 48 + 35)
CAHOOTS
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
COHORTS
(83 = 48 + 35)
SCROOCH
(81 = 46 + 35)
CARHOPS
(81 = 46 + 35)
SCRATCH
(81 = 46 + 35)
TOPARCH
(81 = 46 + 35)
SCRATCH
(81 = 46 + 35)
OCTARCH
(81 = 46 + 35)
OCTARCH
(81 = 46 + 35)
CARHOPS
(81 = 46 + 35)
SCROOCH
(81 = 46 + 35)
TOPARCH
(81 = 46 + 35)
CARPORT
(80 = 45 + 35)
COACTOR
(80 = 45 + 35)
PROCTOR
(80 = 45 + 35)
PROCTOR
(80 = 45 + 35)
COACTOR
(80 = 45 + 35)
Legendary
Words With Friends
PlaysYour Best
Words With Friends
Plays
↑

Words within the letters of scratchproof

2 letter words in scratchproof (14 words)

aharasatfahaofohorospasotato

3 letter words in scratchproof (51 words)

actaftaptarcarsartashaspcapcarcatcoocopcotfarfatfohfopforfrohaphashathophotoafoaroatoftohsoohopsoptorsparpatpotrapratrhorotsacsapsatsopsotspataptartootop

4 letter words in scratchproof (106 words)

actsafroarcharcsartsatopcapscarpcarscartcashcastcatschapcharchatchopcoatcohocoopcooscootcopscostcotscrapcropfactfastfatsfohsfootfopsforaforthapsharphasphatshoarhoofhoophoothopshorohosthotsoafsoarsoathoatsoctooohsoopsoptsorcapactparspartpastpathpatspoohpoorportposhpostpotsprosraftrapsraptrashraspratsrhosroarroofrootrotsscarscatscotshooshopshotsoapsoarsofasoftsootsortsparspatspotstarstoptacotapstarotarptarstopstorotraptsar

5 letter words in scratchproof (98 words)

achooactorafootafrosascotcarpscartscatchchaoschapschaptcharschartchatschopscoachcoactcoastcoatscocoacocoscohoscoopscooptcootscopracorpscostacraftcrapscrashcroftcropsfactsforthfortsfroshfrostfrothharpshoofshoopshootshoroshostaoathsoctosorthooscarpactsparchpartspatchpathsphotopoachpoochpoohsporchportsproofraftsroachroarsroastroofsroostrootsrotorscarfscarpscoopscootscrapshaftsharpshootshortsoftasoothsoporspoofspoorsportspratstaphstoopstrapstroptacostarostarpstorahtorchtorsotrapstrashtroop

6 letter words in scratchproof (38 words)

accostactorscahootcaptorcarhopcarrotcastorchartscoactscoarctcocoascohortcooptscostarcraftscroftscrotchfactorfratchfrothsoratorparrotpastorpathosphotospotashproofsraptorrotorsscorchscotchscrotashofarsophtastarchtorportrocartroops

7 letter words in scratchproof (21 words)

cahootscaptorscarhopscarportcarrotscoactorcoarctscohortscorporafactorsoctarchoratorsparrotsproctorraptorsscratchscroochtoparchtorporstrocarstrochar

8 letter words in scratchproof (9 words)

carportscoactorscofactorcrapshotoctarchsproctorsscrootchtoparchstrochars

9 letter words in scratchproof (3 words)

cofactorscrapshoothoarfrost

10 letter words in scratchproof (1 word)

crashproof

12 letter words in scratchproof (1 word)

scratchproof

scratchproof + 1 blank (1 word)

scratchproofs

scratchproof + 2 blanks (2 words)

scratchproofedscratchproofer
↑

Words containing the sequence scratchproof

Words that start with scratchproof (6 words)

scratchproofscratchproofedscratchprooferscratchproofersscratchproofingscratchproofs

Words with scratchproof in them (1 word)

scratchproof

Words that end with scratchproof (1 word)

scratchproof
↑

Word Growth involving scratchproof

Shorter words in scratchproof

of roof proof

at rat scratch

Longer words containing scratchproof

scratchproofed

scratchproofer scratchproofers

scratchproofing

scratchproofs