Nuprl Lemma : pair-sq-axiom-wf
∀[a,b:Top]. (<a, b> ~ Ax ∈ Type)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
pair: <a, b>,
universe: Type,
sqequal: s ~ t,
axiom: Ax
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
bfalse: ff,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
false: False,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
base_wf,
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
baseClosed,
closedConclusion,
baseApply,
sqequalIntensionalEquality,
voidElimination,
natural_numberEquality,
lambdaFormation,
universeEquality,
pointwiseFunctionalityForEquality,
promote_hyp,
sqequalExtensionalEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
dependent_functionElimination,
independent_functionElimination,
Error :universeIsType,
imageMemberEquality
Latex:
\mforall{}[a,b:Top]. (<a, b> \msim{} Ax \mmember{} Type)
Date html generated:
2019_06_20-PM-00_38_30
Last ObjectModification:
2018_10_15-PM-10_15_07
Theory : list_0
Home
Index