Nuprl Lemma : iseg_member
∀[T:Type]. ∀l1,l2:T List. ∀x:T. (l1 ≤ l2 ⇒ (x ∈ l1) ⇒ (x ∈ l2))
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
iseg_implies_member,
l_member_wf,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. \mforall{}x:T. (l1 \mleq{} l2 {}\mRightarrow{} (x \mmember{} l1) {}\mRightarrow{} (x \mmember{} l2))
Date html generated:
2016_05_14-PM-01_32_21
Last ObjectModification:
2015_12_26-PM-05_25_04
Theory : list_1
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