Nuprl Lemma : sublist_tl2
∀[T:Type]. ∀u:T. ∀v,L1:T List. (L1 ⊆ v ⇒ L1 ⊆ [u / v])
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
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],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
not: ¬A,
top: Top,
false: False
Lemmas referenced :
sublist_wf,
list_wf,
sublist_tl,
cons_wf,
assert_elim,
null_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
assert_wf,
reduce_tl_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}u:T. \mforall{}v,L1:T List. (L1 \msubseteq{} v {}\mRightarrow{} L1 \msubseteq{} [u / v])
Date html generated:
2019_06_20-PM-01_22_45
Last ObjectModification:
2018_09_26-PM-05_23_28
Theory : list_1
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