Nuprl Lemma : set-relation-on_wf
∀[A:Set{i:l}]. ∀[R:{u:Set{i:l}| (u ∈ A)} ⟶ {u:Set{i:l}| (u ∈ A)} ⟶ ℙ']. (SetRelationOn(A;R) ∈ ℙ')
Proof
Definitions occuring in Statement :
set-relation-on: SetRelationOn(A;R),
setmem: (x ∈ s),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
set-relation-on: SetRelationOn(A;R),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
seteq_wf,
setmem_wf,
Set_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
rename,
setElimination,
functionEquality,
lambdaEquality,
hypothesisEquality,
cumulativity,
hypothesis,
setEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Set\{i:l\}]. \mforall{}[R:\{u:Set\{i:l\}| (u \mmember{} A)\} {}\mrightarrow{} \{u:Set\{i:l\}| (u \mmember{} A)\} {}\mrightarrow{} \mBbbP{}']. (SetRelationOn(A;R) \mmember{} \mBbbP{}\000C')
Date html generated:
2018_05_29-PM-01_51_56
Last ObjectModification:
2018_05_25-PM-02_00_01
Theory : constructive!set!theory
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