Nuprl Lemma : coW-item-coWmem
∀[A:𝕌']. ∀B:A ⟶ Type. ∀w:coW(A;a.B[a]). ∀t:coW-dom(a.B[a];w). coWmem(a.B[a];coW-item(w;t);w)
Proof
Definitions occuring in Statement :
coWmem: coWmem(a.B[a];z;w),
coW-item: coW-item(w;b),
coW-dom: coW-dom(a.B[a];w),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
member: t ∈ T,
exists: ∃x:A. B[x],
coWmem: coWmem(a.B[a];z;w),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW-equiv_weakening,
coW_wf,
coW-dom_wf,
coW-item_wf,
coW-equiv_wf
Rules used in proof :
independent_isectElimination,
dependent_functionElimination,
universeEquality,
functionEquality,
cumulativity,
instantiate,
hypothesis,
applyEquality,
lambdaEquality,
sqequalRule,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
dependent_pairFormation,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}B:A {}\mrightarrow{} Type. \mforall{}w:coW(A;a.B[a]). \mforall{}t:coW-dom(a.B[a];w). coWmem(a.B[a];coW-item(w;t);w)
Date html generated:
2018_07_25-PM-01_48_13
Last ObjectModification:
2018_06_20-PM-05_57_58
Theory : co-recursion
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