Nuprl Lemma : assert-co-w-null
∀[A:Type]. ∀[w:co-w(A)]. uiff(↑co-w-null(w);w = w-nil() ∈ co-w(A))
Proof
Definitions occuring in Statement :
w-nil: w-nil(),
co-w-null: co-w-null(w),
co-w: co-w(A),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
wfd-tree2: wfd-tree(A),
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
co-w-null: co-w-null(w),
isl: isl(x),
w-nil: w-nil(),
btrue: tt,
true: True,
implies: P ⇒ Q,
guard: {T},
all: ∀x:A. B[x],
bfalse: ff,
false: False,
unit: Unit,
it: ⋅
Lemmas referenced :
wfd-tree2_wf,
assert_wf,
co-w-null_wf,
assert_witness,
equal-wf-T-base,
co-w_wf,
co-w-ext,
subtype_rel_weakening,
unit_wf2,
equal_wf,
true_wf,
false_wf,
w-nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
applyEquality,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
sqequalRule,
natural_numberEquality,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
independent_functionElimination,
baseClosed,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
universeEquality,
unionEquality,
functionEquality,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
unionElimination,
voidElimination,
equalityElimination
Latex:
\mforall{}[A:Type]. \mforall{}[w:co-w(A)]. uiff(\muparrow{}co-w-null(w);w = w-nil())
Date html generated:
2018_05_21-PM-10_17_58
Last ObjectModification:
2017_07_26-PM-06_36_30
Theory : bar!induction
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