Nuprl Lemma : decide-exception-type
∀[T:Type]. ∀[x:T]. ∀[A,B:Top]. case x of inl(u) => A[u] | inr(v) => B[v] ~ x supposing exception-type(T)
Proof
Definitions occuring in Statement :
exception-type: exception-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
exception-type: exception-type(T),
squash: ↓T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
exception-type_wf,
top_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
sqequalRule,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
axiomSqEquality,
hypothesis,
pointwiseFunctionality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_isectElimination,
closedConclusion,
baseApply,
baseClosed,
imageMemberEquality,
imageElimination,
exceptionSqequal,
axiomEquality,
sqequalExtensionalEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
Error :universeIsType,
sqequalIntensionalEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[A,B:Top].
case x of inl(u) => A[u] | inr(v) => B[v] \msim{} x supposing exception-type(T)
Date html generated:
2019_06_20-AM-11_20_53
Last ObjectModification:
2018_10_15-PM-03_25_59
Theory : call!by!value_1
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