Nuprl Lemma : step-function_wf
∀[T:Type]. ∀[transition:T ⟶ T ⟶ ℙ]. ∀[X:Type]. (step-function(T;transition;X) ∈ Type)
Proof
Definitions occuring in Statement :
step-function: step-function(T;transition;X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
step-function: step-function(T;transition;X),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
exists_wf,
isect2_wf,
isect2_subtype_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[transition:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:Type]. (step-function(T;transition;X) \mmember{} Type)
Date html generated:
2016_05_15-PM-10_11_38
Last ObjectModification:
2015_12_27-PM-05_58_22
Theory : eval!all
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