Nuprl Lemma : has-value-extensionality
∀[a,b:Base]. (a)↓ = (b)↓ ∈ ℙ supposing (a)↓ ⇐⇒ (b)↓
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
base: Base,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
has-value: (a)↓,
prop: ℙ,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
has-value_wf_base,
istype-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqleExtensionalEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
independent_functionElimination,
hypothesis,
Error :universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
Error :productIsType,
Error :functionIsType,
because_Cache,
Error :isect_memberEquality_alt,
axiomEquality,
Error :isectIsTypeImplies,
Error :inhabitedIsType
Latex:
\mforall{}[a,b:Base]. (a)\mdownarrow{} = (b)\mdownarrow{} supposing (a)\mdownarrow{} \mLeftarrow{}{}\mRightarrow{} (b)\mdownarrow{}
Date html generated:
2019_06_20-AM-11_20_34
Last ObjectModification:
2018_10_16-PM-01_47_32
Theory : call!by!value_1
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