Nuprl Lemma : decide_wf
∀[T1,T2,T3:Type]. ∀[x:T1 + T2]. ∀[l:T1 ⟶ T3]. ∀[r:T2 ⟶ T3]. (case x of inl(a) => l[a] | inr(b) => r[b] ∈ T3)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
lambdaFormation,
unionElimination,
sqequalRule,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T1,T2,T3:Type]. \mforall{}[x:T1 + T2]. \mforall{}[l:T1 {}\mrightarrow{} T3]. \mforall{}[r:T2 {}\mrightarrow{} T3].
(case x of inl(a) => l[a] | inr(b) => r[b] \mmember{} T3)
Date html generated:
2019_10_15-AM-11_06_47
Last ObjectModification:
2018_08_21-PM-01_58_34
Theory : general
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