Nuprl Lemma : setimage_wf
∀[x,b:coSet{i:l}]. (setimage{i:l}(x;b) ∈ ℙ')
Proof
Definitions occuring in Statement :
setimage: setimage{i:l}(x;b),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
and: P ∧ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
setimage: setimage{i:l}(x;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
iff_wf,
pi1_wf,
seteq_wf,
all_wf,
setmem_wf,
coSet_wf,
exists_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
lambdaEquality,
hypothesisEquality,
cumulativity,
hypothesis,
productEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x,b:coSet\{i:l\}]. (setimage\{i:l\}(x;b) \mmember{} \mBbbP{}')
Date html generated:
2018_07_29-AM-10_08_37
Last ObjectModification:
2018_07_18-PM-09_11_42
Theory : constructive!set!theory
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