Nuprl Lemma : member_mk_rset_lemma
∀z,P:Top. (z ∈ {x:ℝ | P[x]} ~ P[z])
Proof
Definitions occuring in Statement :
mk-rset: {x:ℝ | P[x]},
rset-member: x ∈ A,
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mk-rset: {x:ℝ | P[x]},
rset-member: x ∈ A
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}z,P:Top. (z \mmember{} \{x:\mBbbR{} | P[x]\} \msim{} P[z])
Date html generated:
2016_05_18-AM-08_08_28
Last ObjectModification:
2015_12_28-AM-01_15_08
Theory : reals
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