Nuprl Lemma : valueall-type_functionality
∀[T,T':Type]. valueall-type(T) ⇐⇒ valueall-type(T') supposing T ≡ T'
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
guard: {T},
has-value: (a)↓,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
ext-eq_wf,
has-value_wf_base,
isect_wf,
uall_wf,
base_wf,
equal-wf-base,
subtype_rel_weakening,
ext-eq_inversion
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lemma_by_obid,
axiomSqleEquality,
because_Cache,
isect_memberEquality,
lambdaEquality,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_pairEquality,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T,T':Type]. valueall-type(T) \mLeftarrow{}{}\mRightarrow{} valueall-type(T') supposing T \mequiv{} T'
Date html generated:
2016_05_13-PM-03_24_22
Last ObjectModification:
2016_01_14-PM-06_45_36
Theory : call!by!value_1
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