Nuprl Lemma : tagged-test_wf
∀[T:Type]. ∀[x:"b":𝔹 |+ "a":ℤ]. (tagged-test(x) ∈ "b":𝔹 |+ "a":ℤ)
Proof
Definitions occuring in Statement :
tagged-test: tagged-test(x),
tagged+: T |+ z:B,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
int: ℤ,
token: "$token",
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tagged-test: tagged-test(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
tagged+: T |+ z:B,
isect2: T1 ⋂ T2,
top: Top,
bfalse: ff,
rev_uimplies: rev_uimplies(P;Q),
eq_atom: x =a y,
assert: ↑b,
true: True,
bnot: ¬bb,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
eq_atom_wf,
tagged-tag_wf2,
tagged+_wf,
top_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert_of_eq_atom,
mk-tagged_wf_unequal,
iff_transitivity,
not_wf,
equal-wf-base,
false_wf,
true_wf,
iff_weakening_uiff,
assert_of_bnot,
bfalse_wf,
mk-tagged_wf,
assert_of_eq_int,
tagged-val_wf2,
isect2_subtype_rel2,
tag-case_wf,
bnot_wf,
eqff_to_assert,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
tokenEquality,
intEquality,
hypothesisEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
atomEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
isect_memberEquality,
independent_pairFormation,
natural_numberEquality,
impliesFunctionality,
voidElimination,
voidEquality,
addEquality,
applyEquality,
dependent_functionElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:"b":\mBbbB{} |+ "a":\mBbbZ{}]. (tagged-test(x) \mmember{} "b":\mBbbB{} |+ "a":\mBbbZ{})
Date html generated:
2018_05_21-PM-08_43_07
Last ObjectModification:
2017_07_26-PM-06_07_02
Theory : general
Home
Index