Nuprl Lemma : l_member-set
∀[T:Type]. ∀L:T List. ∀x:T. ((x ∈ L) ⇒ (x ∈ L))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member-settype,
l_member_wf,
list-subtype,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
dependent_functionElimination,
cumulativity,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
productElimination,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. ((x \mmember{} L) {}\mRightarrow{} (x \mmember{} L))
Date html generated:
2016_05_14-AM-07_49_24
Last ObjectModification:
2015_12_26-PM-04_45_00
Theory : list_1
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