Nuprl Lemma : coWmem_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w':coW(A;a.B[a])]. (coWmem(a.B[a];w;w') ∈ ℙ)
Proof
Definitions occuring in Statement :
coWmem: coWmem(a.B[a];z;w),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
coWmem: coWmem(a.B[a];z;w),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
coW-item_wf,
coW-equiv_wf,
coW-dom_wf,
exists_wf
Rules used in proof :
universeEquality,
functionEquality,
because_Cache,
isect_memberEquality,
cumulativity,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w,w':coW(A;a.B[a])]. (coWmem(a.B[a];w;w') \mmember{} \mBbbP{})
Date html generated:
2018_07_25-PM-01_48_09
Last ObjectModification:
2018_06_20-PM-05_56_55
Theory : co-recursion
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