Nuprl Lemma : R-closed_wf
∀[T:Type]. ∀[X:T ⟶ ℙ]. ∀[R:T ⟶ T ⟶ ℙ]. (R-closed(T;x.X[x];a,b.R[a;b]) ∈ ℙ)
Proof
Definitions occuring in Statement :
R-closed: R-closed(T;x.X[x];a,b.R[a; b]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
R-closed: R-closed(T;x.X[x];a,b.R[a; b]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[X:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R-closed(T;x.X[x];a,b.R[a;b]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_08_51
Last ObjectModification:
2015_12_26-PM-07_54_54
Theory : fan-theorem
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