Nuprl Lemma : mk-tagged_wf_unequal
∀[B:Type]. ∀[tg,a:Atom]. ∀[x:Top]. (mk-tagged(a;x) ∈ tg:B) supposing ¬(tg = a ∈ Atom)
Proof
Definitions occuring in Statement :
mk-tagged: mk-tagged(tg;x),
tag-case: z:T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
member: t ∈ T,
atom: Atom,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
tag-case: z:T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mk-tagged: mk-tagged(tg;x),
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 ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B
Lemmas referenced :
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
top_wf,
not_wf,
equal-wf-base,
atom_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
independent_functionElimination,
equalitySymmetry,
voidElimination,
dependent_pairFormation,
equalityTransitivity,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
axiomEquality,
isect_memberEquality,
atomEquality,
applyEquality,
universeEquality
Latex:
\mforall{}[B:Type]. \mforall{}[tg,a:Atom]. \mforall{}[x:Top]. (mk-tagged(a;x) \mmember{} tg:B) supposing \mneg{}(tg = a)
Date html generated:
2018_05_21-PM-08_42_26
Last ObjectModification:
2017_07_26-PM-06_06_18
Theory : general
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