Nuprl Lemma : mk_lambdas_fun-eta
∀[F:Top]. ∀[m:ℕ]. (mk_lambdas_fun(F;m) ~ mk_lambdas_fun(λg.(F (λx.(g x)));m))
Proof
Definitions occuring in Statement :
mk_lambdas_fun: mk_lambdas_fun(F;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk_lambdas_fun: mk_lambdas_fun(F;m),
top: Top,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
mk_applies: mk_applies(F;G;m),
all: ∀x:A. B[x]
Lemmas referenced :
mk_lambdas-fun-eta,
false_wf,
le_wf,
primrec0_lemma,
nat_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
dependent_functionElimination,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[F:Top]. \mforall{}[m:\mBbbN{}]. (mk\_lambdas\_fun(F;m) \msim{} mk\_lambdas\_fun(\mlambda{}g.(F (\mlambda{}x.(g x)));m))
Date html generated:
2016_05_15-PM-02_10_55
Last ObjectModification:
2015_12_27-AM-00_35_05
Theory : untyped!computation
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