Nuprl Lemma : strong-continuous-tag-case
∀[z:Atom]. ∀[F:Type ⟶ Type]. Continuous+(T.z:F[T]) supposing Continuous+(T.F[T])
Proof
Definitions occuring in Statement :
tag-case: z:T,
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
tag-case: z:T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s],
so_apply: x[s1;s2],
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,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x]
Lemmas referenced :
strong-continuous-depproduct,
ifthenelse_wf,
eq_atom_wf,
top_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,
continuous-constant,
nat_wf,
strong-type-continuous_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
lambdaEquality,
instantiate,
hypothesisEquality,
hypothesis,
universeEquality,
applyEquality,
functionExtensionality,
cumulativity,
independent_isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
isect_memberEquality,
independent_pairEquality,
axiomEquality,
functionEquality
Latex:
\mforall{}[z:Atom]. \mforall{}[F:Type {}\mrightarrow{} Type]. Continuous+(T.z:F[T]) supposing Continuous+(T.F[T])
Date html generated:
2018_05_21-PM-08_42_00
Last ObjectModification:
2017_07_26-PM-06_05_53
Theory : general
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