Nuprl Lemma : cons-l_contains
∀[T:Type]. ∀A,B:T List. ∀x:T. (A ⊆ B ⇒ A ⊆ [x / B])
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
cons: [a / b],
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],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ
Lemmas referenced :
l_contains-append4,
cons_wf,
nil_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
l_contains_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B:T List. \mforall{}x:T. (A \msubseteq{} B {}\mRightarrow{} A \msubseteq{} [x / B])
Date html generated:
2016_05_14-AM-07_55_13
Last ObjectModification:
2015_12_26-PM-04_49_13
Theory : list_1
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