Nuprl Lemma : eqv_mod_subset_wf
∀[g:GrpSig]. ∀[s:|g| ⟶ ℙ]. ∀[a,b:|g|].  (a ≡ b (mod s in g) ∈ ℙ)
Proof
Definitions occuring in Statement : 
eqv_mod_subset: a ≡ b (mod s in g)
, 
grp_car: |g|
, 
grp_sig: GrpSig
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
eqv_mod_subset: a ≡ b (mod s in g)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
infix_ap: x f y
, 
prop: ℙ
Lemmas referenced : 
grp_op_wf, 
grp_inv_wf, 
grp_car_wf, 
grp_sig_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
applyEquality, 
hypothesisEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
functionEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}[g:GrpSig].  \mforall{}[s:|g|  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[a,b:|g|].    (a  \mequiv{}  b  (mod  s  in  g)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-00_09_03
Last ObjectModification:
2015_12_26-PM-11_45_32
Theory : groups_1
Home
Index