Nuprl Lemma : l_subset_append
∀[T:Type]. ∀[L:T List]. ∀L1,L2:T List. (l_subset(T;L1 @ L2;L) ⇐⇒ l_subset(T;L1;L) ∧ l_subset(T;L2;L))
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
l_subset: l_subset(T;as;bs),
member: t ∈ T,
rev_implies: P ⇐ Q,
or: P ∨ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
member_append,
l_member_wf,
l_subset_wf,
append_wf,
and_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
cut,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
lemma_by_obid,
isectElimination,
because_Cache,
productElimination,
inlFormation,
sqequalRule,
inrFormation,
unionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List].
\mforall{}L1,L2:T List. (l\_subset(T;L1 @ L2;L) \mLeftarrow{}{}\mRightarrow{} l\_subset(T;L1;L) \mwedge{} l\_subset(T;L2;L))
Date html generated:
2016_05_14-AM-07_54_04
Last ObjectModification:
2015_12_26-PM-04_48_33
Theory : list_1
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