Nuprl Lemma : nats_wf
nats() ∈ stream(ℕ)
Proof
Definitions occuring in Statement :
nats: nats(),
stream: stream(A),
nat: ℕ,
member: t ∈ T
Definitions unfolded in proof :
nats: nats(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int-valueall-type,
set-valueall-type,
le_wf,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-one-mul-top,
zero-add,
minus-one-mul,
minus-add,
condition-implies-le,
sq_stable__le,
not-le-2,
false_wf,
decidable__le,
nat_wf,
mk-stream_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_pairFormation,
lambdaFormation,
voidElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
introduction,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
isect_memberEquality,
voidEquality,
intEquality,
because_Cache,
minusEquality
Latex:
nats() \mmember{} stream(\mBbbN{})
Date html generated:
2016_05_14-AM-06_23_44
Last ObjectModification:
2016_01_14-PM-08_02_25
Theory : co-recursion
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