Nuprl Lemma : bag-member-spread-to-pi
∀[P:Top × Top]. ∀[C,p,T:Top]. (p ↓∈ let x,y = P in C[x;y] ~ p ↓∈ C[fst(P);snd(P)])
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
pi1: fst(t),
pi2: snd(t),
spread: spread def,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
pi1: fst(t),
pi2: snd(t),
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{} p \mdownarrow{}\mmember{} C[fst(P);snd(P)])
Date html generated:
2016_05_15-PM-02_39_35
Last ObjectModification:
2015_12_27-AM-09_42_33
Theory : bags
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