Nuprl Lemma : bottom-member-approx-type
∀[T:Type]. (T ⇒ (⊥ ∈ approx-type(T)))
Proof
Definitions occuring in Statement :
approx-type: approx-type(T),
bottom: ⊥,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
squash: ↓T,
top: Top,
cand: A c∧ B
Lemmas referenced :
member-approx-type,
equal-wf-base,
sqle_wf_base,
base_wf,
exists_wf,
squash_wf,
bottom-sqle
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaEquality,
sqequalRule,
hypothesisEquality,
hypothesis,
independent_isectElimination,
productElimination,
baseClosed,
dependent_functionElimination,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productEquality,
pointwiseFunctionalityForEquality,
rename,
imageMemberEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_pairFormation
Latex:
\mforall{}[T:Type]. (T {}\mRightarrow{} (\mbot{} \mmember{} approx-type(T)))
Date html generated:
2018_05_21-PM-00_05_24
Last ObjectModification:
2017_12_30-PM-02_27_09
Theory : partial_1
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