Nuprl Lemma : w-bars_wf
∀[A:Type]. ∀[w:co-w(A)]. ∀[p:ℕ ⟶ A]. (w-bars(w;p) ∈ ℙ)
Proof
Definitions occuring in Statement :
w-bars: w-bars(w;p),
co-w: co-w(A),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
w-bars: w-bars(w;p),
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
squash_wf,
exists_wf,
nat_wf,
assert_wf,
co-w-null_wf,
co-w-select_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
upto_wf,
co-w_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
cumulativity,
hypothesisEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
applyEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[w:co-w(A)]. \mforall{}[p:\mBbbN{} {}\mrightarrow{} A]. (w-bars(w;p) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_05_48
Last ObjectModification:
2015_12_27-PM-05_50_35
Theory : bar!induction
Home
Index