Nuprl Lemma : mk_lambdas_unroll_ite
∀[F:Top]. ∀[m:ℕ]. (mk_lambdas(F;m) ~ if (m =z 0) then F else λx.mk_lambdas(F;m - 1) fi )
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
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,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
mk_lambdas: mk_lambdas(F;m),
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
nat_plus: ℕ+,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_base_sq,
int_subtype_base,
primrec0_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
le_wf,
nat_properties,
nequal-le-implies,
zero-add,
mk_lambdas_unroll,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
le-add-cancel,
less_than_wf,
nat_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
instantiate,
cumulativity,
intEquality,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_pairFormation,
promote_hyp,
hypothesis_subsumption,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
lambdaEquality,
sqequalAxiom
Latex:
\mforall{}[F:Top]. \mforall{}[m:\mBbbN{}]. (mk\_lambdas(F;m) \msim{} if (m =\msubz{} 0) then F else \mlambda{}x.mk\_lambdas(F;m - 1) fi )
Date html generated:
2017_10_01-AM-08_40_09
Last ObjectModification:
2017_07_26-PM-04_27_54
Theory : untyped!computation
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