Nuprl Lemma : mk-tagged_wf
∀[B:Type]. ∀[tg:Atom]. ∀[x:B]. (mk-tagged(tg;x) ∈ tg:B)
Proof
Definitions occuring in Statement :
mk-tagged: mk-tagged(tg;x),
tag-case: z:T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom,
universe: Type
Definitions unfolded in proof :
tag-case: z:T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-tagged: mk-tagged(tg;x),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T ,
not: ¬A
Lemmas referenced :
subtype_rel-equal,
ifthenelse_wf,
eq_atom_wf,
top_wf,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
hypothesis,
universeEquality,
cumulativity,
independent_isectElimination,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
axiomEquality,
isect_memberEquality,
atomEquality
Latex:
\mforall{}[B:Type]. \mforall{}[tg:Atom]. \mforall{}[x:B]. (mk-tagged(tg;x) \mmember{} tg:B)
Date html generated:
2018_05_21-PM-08_42_40
Last ObjectModification:
2017_07_26-PM-06_06_32
Theory : general
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