Nuprl Lemma : accessible_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[t:T]. (accessible(T;x,y.R[x;y];t) ∈ ℙ)
Proof
Definitions occuring in Statement :
accessible: accessible(T;x,y.R[x; y];t),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
accessible: accessible(T;x,y.R[x; y];t),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
param-W_wf,
unit_wf2,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
productEquality,
universeEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[t:T]. (accessible(T;x,y.R[x;y];t) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_18_38
Last ObjectModification:
2015_12_26-PM-00_02_55
Theory : co-recursion
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