Nuprl Lemma : copath-nil_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. (() ∈ copath(a.B[a];w))
Proof
Definitions occuring in Statement :
copath-nil: (),
copath: copath(a.B[a];w),
coW: coW(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 :
so_apply: x[s],
so_lambda: λ2x.t[x],
top: Top,
btrue: tt,
ifthenelse: if b then t else f fi ,
subtract: n - m,
eq_int: (i =z j),
coPath: coPath(a.B[a];w;n),
unit: Unit,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
copath: copath(a.B[a];w),
copath-nil: (),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
coPath_wf,
equal-wf-base,
it_wf,
le_wf,
false_wf
Rules used in proof :
universeEquality,
functionEquality,
cumulativity,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
baseClosed,
intEquality,
voidEquality,
voidElimination,
isect_memberEquality,
lambdaEquality,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:coW(A;a.B[a])]. (() \mmember{} copath(a.B[a];w))
Date html generated:
2018_07_25-PM-01_39_29
Last ObjectModification:
2018_06_26-AM-00_25_50
Theory : co-recursion
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