Nuprl Lemma : ispair-member
∀[T:Type]. ∀[t:Base]. ∀[a,b:T]. if t is a pair then a otherwise b ∈ T supposing (t)↓
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
ispair: if z is a pair then a otherwise b,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
top: Top,
prop: ℙ
Lemmas referenced :
base_wf,
top_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
ispairCases,
divergentSqle,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
hypothesisEquality,
sqequalRule,
sqequalAxiom,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:Base]. \mforall{}[a,b:T]. if t is a pair then a otherwise b \mmember{} T supposing (t)\mdownarrow{}
Date html generated:
2016_05_13-PM-03_21_57
Last ObjectModification:
2016_01_14-PM-06_47_15
Theory : call!by!value_1
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