Nuprl Lemma : cbva-intro-test
∀[T:Type]. ∀x:T. T supposing valueall-type(T)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
evalall-reduce,
set-value-type,
equal_wf,
valueall-type-value-type,
istype-universe,
valueall-type_wf,
sq_stable__valueall-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
hypothesisEquality,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
independent_isectElimination,
hypothesis,
cutEval,
Error :dependent_set_memberEquality_alt,
equalityTransitivity,
equalitySymmetry,
Error :equalityIsType1,
Error :inhabitedIsType,
Error :lambdaEquality_alt,
Error :universeIsType,
setElimination,
rename,
hyp_replacement,
applyLambdaEquality,
universeEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[T:Type]. \mforall{}x:T. T supposing valueall-type(T)
Date html generated:
2019_06_20-PM-00_26_54
Last ObjectModification:
2018_10_09-AM-09_14_06
Theory : fun_1
Home
Index