Nuprl Lemma : mk_lambdas_as_lambdas_fun
∀[F:Top]. ∀[m:ℕ]. (mk_lambdas(F;m) ~ mk_lambdas_fun(λg.F;m))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
mk_lambdas_fun: mk_lambdas_fun(F;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
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),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
top: Top,
true: True,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
mk_applies: mk_applies(F;G;m),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
mk_lambdas: mk_lambdas(F;m),
mk_lambdas-fun: mk_lambdas-fun(F;G;n;m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
false_wf,
le_wf,
true_wf,
subtype_base_sq,
nat_wf,
set_subtype_base,
int_subtype_base,
primrec0_lemma,
nat_properties,
decidable__equal_int,
subtract_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
itermAdd_wf,
int_term_value_add_lemma,
equal_wf,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
less_than_wf,
top_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
primrec-unroll,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
mk_applies_roll
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
rename,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
instantiate,
cumulativity,
independent_isectElimination,
intEquality,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
unionElimination,
int_eqEquality,
computeAll,
addEquality,
intWeakElimination,
sqequalAxiom,
equalityElimination,
promote_hyp
Latex:
\mforall{}[F:Top]. \mforall{}[m:\mBbbN{}]. (mk\_lambdas(F;m) \msim{} mk\_lambdas\_fun(\mlambda{}g.F;m))
Date html generated:
2017_10_01-AM-08_40_58
Last ObjectModification:
2017_07_26-PM-04_28_19
Theory : untyped!computation
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