Nuprl Lemma : l_subset_append2
∀[T:Type]. ∀L1,L2,L1',L2':T List. ((l_subset(T;L1;L1') ∧ l_subset(T;L2;L2')) ⇒ l_subset(T;L1 @ L2;L1' @ L2'))
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],
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
prop: ℙ,
l_subset: l_subset(T;as;bs),
or: P ∨ Q,
guard: {T}
Lemmas referenced :
l_subset_append,
append_wf,
l_subset_wf,
list_wf,
member_append,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
cumulativity,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
productEquality,
universeEquality,
because_Cache,
inlFormation,
sqequalRule,
inrFormation
Latex:
\mforall{}[T:Type]
\mforall{}L1,L2,L1',L2':T List.
((l\_subset(T;L1;L1') \mwedge{} l\_subset(T;L2;L2')) {}\mRightarrow{} l\_subset(T;L1 @ L2;L1' @ L2'))
Date html generated:
2017_02_20-AM-10_47_48
Last ObjectModification:
2017_01_22-PM-05_49_51
Theory : list_1
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