Nuprl Lemma : sq_stable__l-ordered
∀[T:Type]. ∀[L:T List]. ∀[R:T ⟶ T ⟶ ℙ]. ((∀x,y:T. SqStable(R[x;y])) ⇒ SqStable(l-ordered(T;x,y.R[x;y];L)))
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
list: T List,
sq_stable: SqStable(P),
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 :
l-ordered: l-ordered(T;x,y.R[x; y];L),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable__all,
all_wf,
l_before_wf,
sq_stable_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
applyEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
((\mforall{}x,y:T. SqStable(R[x;y])) {}\mRightarrow{} SqStable(l-ordered(T;x,y.R[x;y];L)))
Date html generated:
2016_05_15-PM-04_36_06
Last ObjectModification:
2015_12_27-PM-02_45_35
Theory : general
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