Nuprl Lemma : member-sub-mset
∀[T:Type]. ∀L1,L2:T List. (sub-mset(T; L1; L2) ⇒ (∀x:T. ((x ∈ L1) ⇒ (x ∈ L2))))
Proof
Definitions occuring in Statement :
sub-mset: sub-mset(T; 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,
prop: ℙ,
l_contains: A ⊆ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
guard: {T}
Lemmas referenced :
sub-mset-contains,
l_member_wf,
sub-mset_wf,
list_wf,
l_all_iff
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,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (sub-mset(T; L1; L2) {}\mRightarrow{} (\mforall{}x:T. ((x \mmember{} L1) {}\mRightarrow{} (x \mmember{} L2))))
Date html generated:
2016_05_15-PM-04_31_56
Last ObjectModification:
2015_12_27-PM-02_49_02
Theory : general
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