Nuprl Lemma : l-ordered-sublist
∀[A:Type]. ∀R:A ⟶ A ⟶ ℙ. ∀as,bs:A List. (as ⊆ bs ⇒ l-ordered(A;x,y.R[x;y];bs) ⇒ l-ordered(A;x,y.R[x;y];as))
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
l-ordered: l-ordered(T;x,y.R[x; y];L),
member: t ∈ T,
guard: {T},
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
l_before_sublist,
l_before_wf,
l-ordered_wf,
sublist_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
cut,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
lemma_by_obid,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]
\mforall{}R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}. \mforall{}as,bs:A List.
(as \msubseteq{} bs {}\mRightarrow{} l-ordered(A;x,y.R[x;y];bs) {}\mRightarrow{} l-ordered(A;x,y.R[x;y];as))
Date html generated:
2016_05_15-PM-04_38_57
Last ObjectModification:
2015_12_27-PM-02_42_01
Theory : general
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