Nuprl Lemma : bag-member-spread
∀[P:Top × Top]. ∀[C,p,T:Top].  (p ↓∈ let x,y = P in C[x;y] ~ let x,y = P in p ↓∈ C[x;y])
Proof
Definitions occuring in Statement : 
bag-member: x ↓∈ bs
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s1;s2]
, 
spread: spread def, 
product: x:A × B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
top_wf
Rules used in proof : 
productElimination, 
thin, 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
cut, 
lemma_by_obid, 
hypothesis, 
because_Cache, 
productEquality, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
hypothesisEquality
Latex:
\mforall{}[P:Top  \mtimes{}  Top].  \mforall{}[C,p,T:Top].    (p  \mdownarrow{}\mmember{}  let  x,y  =  P  in  C[x;y]  \msim{}  let  x,y  =  P  in  p  \mdownarrow{}\mmember{}  C[x;y])
Date html generated:
2016_05_15-PM-02_39_30
Last ObjectModification:
2015_12_27-AM-09_42_30
Theory : bags
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