Nuprl Lemma : altW_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. (altW(A;a.B[a]) ∈ 𝕌')
Proof
Definitions occuring in Statement :
altW: altW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
altW: altW(A;a.B[a]),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW-wfdd_wf,
coW_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
universeEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
cumulativity,
lambdaEquality,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. (altW(A;a.B[a]) \mmember{} \mBbbU{}')
Date html generated:
2018_07_29-AM-09_22_02
Last ObjectModification:
2018_07_26-PM-05_31_41
Theory : co-recursion
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