Nuprl Lemma : mk_lambdas_fun-unroll-first
∀[F:Top]. ∀[m:ℕ+]. (mk_lambdas_fun(F;m) ~ λx.mk_lambdas_fun(λg.(F (λf.(g (f x))));m - 1))
Proof
Definitions occuring in Statement :
mk_lambdas_fun: mk_lambdas_fun(F;m),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
subtract: n - m,
natural_number: $n,
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,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
mk_applies: mk_applies(F;G;m),
nat: ℕ
Lemmas referenced :
mk_lambdas-fun-shift-init,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
itermSubtract_wf,
intformle_wf,
decidable__le,
subtract_wf,
le_wf,
top_wf,
nat_plus_wf,
primrec1_lemma,
primrec0_lemma,
lelt_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
false_wf,
mk_lambdas-fun-unroll-first
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[F:Top]. \mforall{}[m:\mBbbN{}\msupplus{}]. (mk\_lambdas\_fun(F;m) \msim{} \mlambda{}x.mk\_lambdas\_fun(\mlambda{}g.(F (\mlambda{}f.(g (f x))));m - 1))
Date html generated:
2016_05_15-PM-02_11_16
Last ObjectModification:
2016_01_15-PM-10_20_10
Theory : untyped!computation
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