Nuprl Lemma : mk_lambdas_fun_compose2
∀[f:Top]. ∀[m:ℕ]. ∀[n:ℕm + 1].
(mk_lambdas_fun(λh,x. (h mk_lambdas_fun(f;n));m) ~ mk_lambdas_fun(λg.mk_lambdas_fun(λh,x. (h (f g));m - n);n))
Proof
Definitions occuring in Statement :
mk_lambdas_fun: mk_lambdas_fun(F;m),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
subtract: n - m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
mk_lambdas: mk_lambdas(F;m),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
mk_lambdas_fun_compose1,
false_wf,
le_wf,
primrec1_lemma,
int_seg_wf,
nat_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
addEquality,
setElimination,
rename,
because_Cache
Latex:
\mforall{}[f:Top]. \mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m + 1].
(mk\_lambdas\_fun(\mlambda{}h,x. (h mk\_lambdas\_fun(f;n));m)
\msim{} mk\_lambdas\_fun(\mlambda{}g.mk\_lambdas\_fun(\mlambda{}h,x. (h (f g));m - n);n))
Date html generated:
2016_05_15-PM-02_11_33
Last ObjectModification:
2015_12_27-AM-00_34_38
Theory : untyped!computation
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