Nuprl Lemma : groups_1 |
13,42 |
|
ABS: IsMonoid(T;op;id)
STM: monoid p wf
STM: sq stable monoid p
ABS: IsGroup(T;op;id;inv)
STM: group p wf
STM: sq stable group p
DIR: grp sig object directory
STM: grp sig inc
STM: comb for grp car wf
STM: grp op l
STM: grp op r
ABS: IMonoid
STM: imon wf
STM: mk imon
STM: imon properties
STM: imon all properties
STM: mon ident
STM: mon assoc
ABS: Mon
STM: mon wf
STM: mk mon
STM: mon properties
STM: assert of mon eq
STM: decidable mon eq
STM: grp eq sym
ABS: IAbMonoid
STM: iabmonoid wf
STM: iabmonoid properties
STM: abmonoid comm
STM: abmonoid ac 1
ABS: AbMon
STM: abmonoid wf
STM: mk abmonoid
STM: abmonoid inc
STM: abmonoid properties
ABS: IGroup
STM: igrp wf
STM: igrp properties
ABS: mk_igrp(T;op;id;inv)
STM: mk igrp wf
STM: grp inverse
STM: grp op cancel l
STM: grp op cancel r
STM: grp inv id
STM: grp inv inv
STM: grp inv assoc
STM: grp inv thru op
STM: grp eq op l
STM: grp eq op r
STM: grp eq shift right
STM: grp inv diff
ABS: Group{i}
STM: grp wf
STM: mk grp
STM: grp properties
ABS: s SubGrp of g
STM: subgrp p wf
ABS: norm_subset_p(g;s)
STM: norm subset p wf
ABS: NormSubGrp{i}(g)
STM: norm subgrp wf
ABS: a
b (mod s in g)
STM: eqv mod subset wf
STM: eqv mod subset is eqv
ABS: IAbGrp{i}
STM: iabgrp wf
STM: iabgrp op inv assoc
STM: iabgrp properties
ABS: |g//h|
ABS: AbGrp
STM: abgrp wf
STM: abgrp properties
ABS: IsMonHom{M1,M2}(f)
STM: monoid hom p wf
ABS: IsMonHomInj(g;h;f)
STM: mon hom inj p wf
ABS: MonHom(M1,M2)
STM: monoid hom wf
STM: sq stable monoid hom p
STM: monoid hom properties
STM: monoid hom id
STM: monoid hom op
STM: grp hom formation
STM: grp hom inv
ABS: InjMonHom(g;h)
STM: inj mon hom wf
STM: inj mon hom properties
STM: ident mon hom shift
STM: inverse grp sig hom shift
STM: mon hom p id
STM: mon hom p comp
STM: tidentity wf for mon hom
STM: compose wf for mon hom
STM: comb for compose wf for mon hom
ABS: g
set
STM: dset of mon wf0
STM: dset of mon wf
ABS: OMon
STM: omon wf
STM: omon properties
ABS: OCMon
STM: ocmon wf
STM: ocmon properties
STM: ocmon refl
STM: ocmon trans
STM: ocmon anti sym
STM: ocmon connex
STM: ocmon cancel
STM: ocmon 6
ABS: g
oset
STM: oset of ocmon wf0
STM: oset of ocmon wf
STM: dset of mon wf2
ABS: a
b
STM: grp leq wf
STM: comb for grp leq wf
STM: sq stable grp leq
ABS: a < b
STM: grp lt wf
STM: comb for grp lt wf
STM: grp leq iff lt or eq
STM: decidable grp lt
STM: grp lt is sp of leq a
STM: grp lt trans
STM: grp lt irreflexivity
STM: grp lt transitivity 2
STM: grp lt transitivity 1
STM: grp leq weakening eq
STM: grp leq weakening lt
STM: grp leq transitivity
STM: omon lt mono imp leq mono
STM: grp leq antisymmetry
STM: grp leq complement
STM: grp lt complement
STM: grp lt trichot
STM: grp op preserves le
STM: grp op preserves lt
ABS: OGrp
STM: ocgrp wf
STM: ocgrp properties
STM: ocgrp inverse
STM: grp leq op l
STM: grp lt op l
STM: grp op polarity
ABS: a <
b
STM: grp blt wf
STM: assert of grp blt
STM: grp lt shift right
STM: grp leq shift right
STM: inj into ocmon
ABS: |g|
STM: hgrp car wf
STM: hgrp car properties
STM: grp op wf2
STM: grp id wf2
ABS: g
hgrp
STM: hgrp of ocgrp wf
STM: hgrp of ocgrp wf2
ABS:
(op,id) lb
i < ub. E(i)
STM: itop wf
STM: comb for itop wf
STM: itop aux wf
STM: itop unroll base
STM: itop unroll hi
STM: itop unroll unit
STM: itop unroll lo
STM: itop shift
STM: itop split
ABS: n x(op;id) e
STM: nat op wf
STM: comb for nat op wf
STM: nat op zero
STM: nat op add
ABS: i x(op;id;inv) e
STM: int op wf
STM: comb for int op wf
STM: int op minus
ABS:
lb
i < ub. E(i)
STM: mon itop wf
STM: comb for mon itop wf
STM: mon itop unroll base
STM: mon itop unroll hi
STM: mon itop unroll unit
STM: mon itop unroll lo
STM: mon itop shift
STM: mon itop split
STM: mon itop split el
STM: mon itop op
ABS: n
e
STM: mon nat op wf
STM: comb for mon nat op wf
STM: mon nat op zero
STM: mon nat op unroll
STM: mon nat op one
STM: mon nat op id
STM: mon nat op op
STM: mon nat op add
STM: mon nat op hom swap
STM: mon nat op mul
ABS: (<o,Id> monoid on T)
STM: comp id mon wf
ABS: <
,
>
STM: bor mon wf
ABS: <
,
>
STM: band mon wf
ABS: <
+>
STM: int add grp wf
STM: int add grp wf2
ABS: <
,+>
STM: nat add mon wf
STM: nat int grp sig hom
STM: nat add mon wf2
STM: nat op mon hom 1
STM: nat op mon hom 2
STM: nat op on nat add mon
ABS: <
,*>
STM: int mul mon wf
ABS: when b. p
STM: mon when wf
STM: comb for mon when wf
STM: mon when false
STM: mon when true
STM: mon when of id
STM: mon when thru op
STM: mon when when
STM: mon when swap
STM: mon when is hom
STM: mon when hom swap
STM: nat inc
STM: grp car inc
ABS: zhgrp(n)
STM: int hgrp el wf
ABS: nat(n)
STM: int hgrp to nat wf
STM: zhgrp to nat is hom
STM: zhgrp op mon hom 1
STM: mon nat op wf2
STM: comb for mon nat op wf2