Nuprl Lemma : bar-converges_functionality
∀[T:Type]. ∀[x,y:bar-base(T)]. ∀[a:T]. (bar-equal(T;x;y) ⇒ {x↓a ⇐⇒ x↓a})
Proof
Definitions occuring in Statement :
bar-equal: bar-equal(T;x;y),
bar-converges: x↓a,
bar-base: bar-base(T),
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
bar-converges_wf,
bar-equal_wf,
bar-base_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:bar-base(T)]. \mforall{}[a:T]. (bar-equal(T;x;y) {}\mRightarrow{} \{x\mdownarrow{}a \mLeftarrow{}{}\mRightarrow{} x\mdownarrow{}a\})
Date html generated:
2016_05_14-AM-06_20_34
Last ObjectModification:
2015_12_26-PM-00_00_38
Theory : co-recursion
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