Nuprl Lemma : quot_grp_car_wf
∀g:IGroup. ∀h:NormSubGrp{i}(g).  (|g//h| ∈ Type)
Proof
Definitions occuring in Statement : 
quot_grp_car: |g//h|
, 
norm_subgrp: NormSubGrp{i}(g)
, 
igrp: IGroup
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
norm_subgrp: NormSubGrp{i}(g)
, 
quot_grp_car: |g//h|
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
igrp: IGroup
, 
imon: IMonoid
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
guard: {T}
, 
subgrp_p: s SubGrp of g
Lemmas referenced : 
quotient_wf, 
grp_car_wf, 
eqv_mod_subset_wf, 
eqv_mod_subset_is_eqv, 
norm_subgrp_wf, 
igrp_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
productElimination, 
lemma_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
lambdaEquality, 
because_Cache, 
independent_isectElimination, 
dependent_functionElimination, 
independent_functionElimination, 
applyEquality
Latex:
\mforall{}g:IGroup.  \mforall{}h:NormSubGrp\{i\}(g).    (|g//h|  \mmember{}  Type)
Date html generated:
2016_05_15-PM-00_09_19
Last ObjectModification:
2015_12_26-PM-11_45_40
Theory : groups_1
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