Nuprl Lemma : nth-nats
∀n:ℕ. (s-nth(n;nats()) ~ n)
Proof
Definitions occuring in Statement :
nats: nats(),
s-nth: s-nth(n;s),
nat: ℕ,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
nats: nats(),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
nat: ℕ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
false: False,
ge: i ≥ j ,
le: A ≤ B,
cand: A c∧ B,
less_than: a < b,
s-nth: s-nth(n;s),
mk-stream: mk-stream(f;x),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
not: ¬A,
has-value: (a)↓,
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a)
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
istype-universe,
subtype_rel_self,
iff_weakening_equal,
add-zero,
istype-nat,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
istype-less_than,
zero-add,
subtract-1-ge-0,
eq_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
le_weakening,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
istype-assert,
istype-void,
value-type-has-value,
int-value-type,
subtract_wf,
valueall-type-has-valueall,
int-valueall-type,
evalall-reduce,
add-associates,
add-swap,
add-commutes,
add-comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
applyEquality,
lambdaEquality_alt,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
universeEquality,
dependent_functionElimination,
natural_numberEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
because_Cache,
productElimination,
independent_functionElimination,
intWeakElimination,
independent_pairFormation,
voidElimination,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
callbyvalueReduce,
sqleReflexivity,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
equalityIstype,
sqequalBase,
functionIsType,
addEquality,
Error :memTop
Latex:
\mforall{}n:\mBbbN{}. (s-nth(n;nats()) \msim{} n)
Date html generated:
2020_05_19-PM-09_36_54
Last ObjectModification:
2019_12_31-PM-00_59_15
Theory : co-recursion
Home
Index