Nuprl Lemma : l_contains-member
∀[T:Type]. ∀A,B:T List. (A ⊆ B ⇒ {∀x:T. ((x ∈ A) ⇒ (x ∈ B))})
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_contains: A ⊆ B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
guard: {T}
Lemmas referenced :
l_all_iff,
l_member_wf,
l_all_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
setElimination,
rename,
hypothesis,
setEquality,
productElimination,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B:T List. (A \msubseteq{} B {}\mRightarrow{} \{\mforall{}x:T. ((x \mmember{} A) {}\mRightarrow{} (x \mmember{} B))\})
Date html generated:
2016_05_14-AM-07_53_28
Last ObjectModification:
2015_12_26-PM-04_47_29
Theory : list_1
Home
Index