Nuprl Lemma : tagged-val_wf2
∀[B:Type]. ∀[z:Atom]. ∀[x:z:B]. x.val ∈ B supposing x.tag = z ∈ Atom
Proof
Definitions occuring in Statement :
tagged-val: x.val,
tagged-tag: x.tag,
tag-case: z:T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
tagged-tag: x.tag,
pi1: fst(t),
tag-case: z:T,
tagged-val: x.val,
pi2: snd(t),
subtype_rel: A ⊆r B,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
tag-case_wf,
equal-wf-T-base,
atom_subtype_base,
eq_atom_wf,
equal-wf-base,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
extract_by_obid,
cumulativity,
atomEquality,
productElimination,
applyEquality,
universeEquality,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
unionElimination,
instantiate,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
impliesFunctionality
Latex:
\mforall{}[B:Type]. \mforall{}[z:Atom]. \mforall{}[x:z:B]. x.val \mmember{} B supposing x.tag = z
Date html generated:
2018_05_21-PM-08_42_13
Last ObjectModification:
2017_07_26-PM-06_06_05
Theory : general
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