Nuprl Lemma : co-w-null_wf
∀[A:Type]. ∀[w:co-w(A)]. (co-w-null(w) ∈ 𝔹)
Proof
Definitions occuring in Statement :
co-w-null: co-w-null(w),
co-w: co-w(A),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
co-w-null: co-w-null(w)
Lemmas referenced :
co-w-ext,
co-w_wf,
subtype_rel_weakening,
unit_wf2,
equal_wf,
isl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality,
because_Cache,
universeEquality,
applyEquality,
unionEquality,
functionEquality,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[w:co-w(A)]. (co-w-null(w) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-10_17_53
Last ObjectModification:
2017_07_26-PM-06_36_28
Theory : bar!induction
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