Nuprl Lemma : destructor-sum
∀[F,G:Type ⟶ Type]. (destructor{i:l}(T.F[T]) ⇒ destructor{i:l}(T.G[T]) ⇒ destructor{i:l}(T.F[T] + G[T]))
Proof
Definitions occuring in Statement :
destructor: destructor{i:l}(T.F[T]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
destructor: destructor{i:l}(T.F[T]),
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
decomp: decomp{i:l}(S.F[S];T;x),
constructor: Constr(T.F[T]),
subtype_rel: A ⊆r B,
ap-con: ap-con(con;L),
prop: ℙ
Lemmas referenced :
subtype_rel_wf,
base_wf,
decomp_wf,
list_wf,
equal_wf,
ap-con_wf,
destructor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
rename,
introduction,
sqequalHypSubstitution,
isect_memberEquality,
cut,
isectElimination,
setElimination,
thin,
dependent_set_memberEquality,
because_Cache,
hypothesis,
extract_by_obid,
cumulativity,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
applyEquality,
functionExtensionality,
universeEquality,
sqequalRule,
lambdaEquality,
unionElimination,
productElimination,
dependent_pairEquality,
inlEquality,
isectEquality,
setEquality,
addLevel,
levelHypothesis,
unionEquality,
instantiate,
dependent_functionElimination,
independent_functionElimination,
inrEquality
Latex:
\mforall{}[F,G:Type {}\mrightarrow{} Type].
(destructor\{i:l\}(T.F[T]) {}\mRightarrow{} destructor\{i:l\}(T.G[T]) {}\mRightarrow{} destructor\{i:l\}(T.F[T] + G[T]))
Date html generated:
2018_05_21-PM-08_45_07
Last ObjectModification:
2017_07_26-PM-06_08_53
Theory : general
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