Nuprl Lemma : seq-single_wf
∀[T:Type]. ∀[t:T]. (seq-single(t) ∈ ℕ1 ⟶ T)
Proof
Definitions occuring in Statement :
seq-single: seq-single(t),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
seq-single: seq-single(t),
int_seg: {i..j-},
false: False,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
or: P ∨ Q,
sq_stable: SqStable(P),
lelt: i ≤ j < k,
squash: ↓T,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
int_seg_wf,
le-add-cancel2,
add-associates,
minus-zero,
minus-add,
add-commutes,
condition-implies-le,
less-iff-le,
le-add-cancel,
add-zero,
zero-add,
add_functionality_wrt_le,
sq_stable__le,
not-equal-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
int_eqEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lemma_by_obid,
dependent_functionElimination,
productElimination,
independent_isectElimination,
unionElimination,
isectElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
addEquality,
voidElimination,
minusEquality,
applyEquality,
isect_memberEquality,
voidEquality,
intEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:T]. (seq-single(t) \mmember{} \mBbbN{}1 {}\mrightarrow{} T)
Date html generated:
2016_05_13-PM-03_48_25
Last ObjectModification:
2016_01_14-PM-07_00_34
Theory : bar-induction
Home
Index