Nuprl Lemma : l_subset_transitivity
∀[T:Type]. ∀A,B,C:T List. (l_subset(T;A;B) ⇒ l_subset(T;B;C) ⇒ l_subset(T;A;C))
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
l_contains_wf,
l_subset-l_contains,
l_subset_wf,
list_wf,
l_contains_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
addLevel,
impliesFunctionality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B,C:T List. (l\_subset(T;A;B) {}\mRightarrow{} l\_subset(T;B;C) {}\mRightarrow{} l\_subset(T;A;C))
Date html generated:
2016_05_14-AM-07_54_21
Last ObjectModification:
2015_12_26-PM-04_48_37
Theory : list_1
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