Nuprl Lemma : union-discrete
∀A,B:Type. (discrete-type(A) ⇒ discrete-type(B) ⇒ discrete-type(A + B))
Proof
Definitions occuring in Statement :
discrete-type: discrete-type(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
discrete-type: discrete-type(T),
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
guard: {T},
sq_type: SQType(T),
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q
Lemmas referenced :
equal_wf,
real_wf,
all_wf,
req_wf,
discrete-type_wf,
inl-one-one,
not-0-eq-1,
inr-one-one,
decide_wf,
top_wf,
int-discrete,
subtype_base_sq,
int_subtype_base,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
applyEquality,
hypothesisEquality,
thin,
unionEquality,
unionElimination,
because_Cache,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
lambdaEquality,
functionEquality,
universeEquality,
productElimination,
independent_isectElimination,
applyLambdaEquality,
natural_numberEquality,
voidElimination,
inlEquality,
hyp_replacement,
instantiate,
cumulativity,
intEquality,
promote_hyp,
imageElimination,
imageMemberEquality,
baseClosed,
inrEquality
Latex:
\mforall{}A,B:Type. (discrete-type(A) {}\mRightarrow{} discrete-type(B) {}\mRightarrow{} discrete-type(A + B))
Date html generated:
2019_10_30-AM-07_17_59
Last ObjectModification:
2018_08_21-PM-03_33_41
Theory : reals
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