Nuprl Lemma : imp-type_wf
∀[A,B:Type]. (imp-type(A;B) ∈ Type)
Proof
Definitions occuring in Statement :
imp-type: imp-type(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imp-type: imp-type(A;B),
so_lambda: λ2x y.t[x; y],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
quotient_wf,
base_wf,
least-equiv_wf,
equal-wf-base,
least-equiv-is-equiv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
hypothesis,
Error :lambdaEquality_alt,
applyEquality,
because_Cache,
functionEquality,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
universeEquality
Latex:
\mforall{}[A,B:Type]. (imp-type(A;B) \mmember{} Type)
Date html generated:
2019_06_20-PM-02_01_41
Last ObjectModification:
2018_10_14-PM-05_23_45
Theory : relations2
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