Nuprl Lemma : s-sub_wf
∀[T:Type]. ∀[s,t:stream(T)]. (s-sub(T;s;t) ∈ ℙ)
Proof
Definitions occuring in Statement :
s-sub: s-sub(T;s;t),
stream: stream(A),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-sub: s-sub(T;s;t),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
all_wf,
less_than_wf,
decidable__le,
istype-false,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
istype-void,
istype-int,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
istype-le,
istype-nat,
equal_wf,
s-nth_wf,
stream_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
functionEquality,
hypothesis,
Error :lambdaEquality_alt,
productEquality,
applyEquality,
hypothesisEquality,
because_Cache,
Error :dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
voidElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
imageElimination,
Error :isect_memberEquality_alt,
minusEquality,
Error :functionIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
Error :universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s,t:stream(T)]. (s-sub(T;s;t) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_37_53
Last ObjectModification:
2018_11_29-PM-05_18_13
Theory : co-recursion
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