Nuprl Lemma : set-relation-on-setrel
∀R,A:Set{i:l}. SetRelationOn(A;setrel(R))
Proof
Definitions occuring in Statement :
setrel: setrel(R),
set-relation-on: SetRelationOn(A;R),
Set: Set{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
setrel: setrel(R),
set-relation-on: SetRelationOn(A;R),
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
setmem_functionality_1,
set-subtype-coSet,
orderedpairset_wf,
subtype_rel_set,
Set_wf,
coSet_wf,
setmem_wf,
orderedpairset_functionality,
seteq_weakening,
seteq_inversion,
seteq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
isectElimination,
instantiate,
lambdaEquality_alt,
cumulativity,
because_Cache,
inhabitedIsType,
independent_isectElimination,
independent_functionElimination,
productElimination,
universeIsType,
setIsType
Latex:
\mforall{}R,A:Set\{i:l\}. SetRelationOn(A;setrel(R))
Date html generated:
2020_05_20-PM-01_19_17
Last ObjectModification:
2020_01_06-PM-01_23_33
Theory : constructive!set!theory
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