Nuprl Lemma : w-nil_wf
∀[A:Type]. (w-nil() ∈ wfd-tree(A))
Proof
Definitions occuring in Statement :
w-nil: w-nil(),
wfd-tree2: wfd-tree(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
w-nil: w-nil(),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
wfd-tree2: wfd-tree(A),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
w-bars: w-bars(w;p),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
co-w-null: co-w-null(w),
isl: isl(x),
co-w-select: w@s,
bor: p ∨bq,
null: null(as),
map: map(f;as),
list_ind: list_ind,
upto: upto(n),
from-upto: [n, m),
lt_int: i <z j,
bfalse: ff,
nil: [],
it: ⋅,
btrue: tt,
true: True,
squash: ↓T
Lemmas referenced :
upto_wf,
int_seg_subtype_nat,
subtype_rel_dep_function,
int_seg_wf,
map_wf,
co-w-select_wf,
co-w-null_wf,
assert_wf,
le_wf,
false_wf,
w-bars_wf,
all_wf,
nat_wf,
subtype_rel_weakening,
unit_wf2,
ext-eq_inversion,
co-w_wf,
it_wf,
co-w-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inlEquality,
hypothesis,
functionEquality,
applyEquality,
unionEquality,
independent_isectElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
lambdaEquality,
axiomEquality,
universeEquality,
dependent_pairFormation,
natural_numberEquality,
independent_pairFormation,
cumulativity,
because_Cache,
setElimination,
rename,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[A:Type]. (w-nil() \mmember{} wfd-tree(A))
Date html generated:
2016_05_15-PM-10_05_55
Last ObjectModification:
2016_01_16-PM-04_05_36
Theory : bar!induction
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