Nuprl Lemma : mk_applies_lambdas_fun0
∀[F,G:Top]. ∀[m:ℕ]. (mk_applies(mk_lambdas_fun(F;m);G;m) ~ F (λx.mk_applies(x;G;m)))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
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,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
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],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
ge: i ≥ j ,
sq_type: SQType(T),
guard: {T},
mk_lambdas_fun: mk_lambdas_fun(F;m),
mk_lambdas-fun: mk_lambdas-fun(F;G;n;m),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_le_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
bool_cases,
int_formula_prop_le_lemma,
intformle_wf,
le_wf,
not_wf,
bnot_wf,
assert_wf,
le_int_wf,
top_wf,
nat_wf,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
itermSubtract_wf,
intformeq_wf,
decidable__equal_int,
nat_properties,
int_subtype_base,
subtype_base_sq,
lelt_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__lt,
mk_applies_lambdas_fun
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality,
independent_pairFormation,
hypothesis,
dependent_functionElimination,
addEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
productElimination,
because_Cache,
instantiate,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
cumulativity,
lambdaFormation,
impliesFunctionality
Latex:
\mforall{}[F,G:Top]. \mforall{}[m:\mBbbN{}]. (mk\_applies(mk\_lambdas\_fun(F;m);G;m) \msim{} F (\mlambda{}x.mk\_applies(x;G;m)))
Date html generated:
2016_05_15-PM-02_11_43
Last ObjectModification:
2016_01_15-PM-10_20_02
Theory : untyped!computation
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