Nuprl Lemma : sq_stable__trans
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ((∀x,y:T. SqStable(R[x;y])) ⇒ SqStable(Trans(T;y,x.R[x;y])))
Proof
Definitions occuring in Statement :
trans: Trans(T;x,y.E[x; y]),
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 :
trans: Trans(T;x,y.E[x; y]),
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],
subtype_rel: A ⊆r B
Lemmas referenced :
sq_stable__all,
all_wf,
sq_stable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
cumulativity,
functionEquality,
applyEquality,
functionExtensionality,
hypothesis,
independent_functionElimination,
because_Cache,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x,y:T. SqStable(R[x;y])) {}\mRightarrow{} SqStable(Trans(T;y,x.R[x;y])))
Date html generated:
2016_10_21-AM-09_42_39
Last ObjectModification:
2016_08_01-PM-09_48_53
Theory : rel_1
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