Nuprl Lemma : retractible_wf
∀[T:Type]. retractible(T) ∈ ℙ supposing T ⊆r Base
Proof
Definitions occuring in Statement :
retractible: retractible(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
retractible: retractible(T),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
exists_wf,
base_wf,
and_wf,
all_wf,
equal-wf-base-T,
has-value_wf_base,
equal-wf-base,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :lambdaEquality_alt,
hypothesisEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
Error :universeIsType,
functionEquality,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
universeEquality
Latex:
\mforall{}[T:Type]. retractible(T) \mmember{} \mBbbP{} supposing T \msubseteq{}r Base
Date html generated:
2019_06_20-AM-11_28_21
Last ObjectModification:
2018_09_28-PM-03_22_47
Theory : call!by!value_2
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