Nuprl Lemma : Wsup_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[a:A]. ∀[b:B[a] ⟶ W(A;a.B[a])]. (Wsup(a;b) ∈ W(A;a.B[a]))
Proof
Definitions occuring in Statement :
Wsup: Wsup(a;b),
W: W(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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Wsup: Wsup(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
W-ext,
W_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality,
applyEquality,
hypothesisEquality,
productElimination,
dependent_pairEquality,
functionEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[a:A]. \mforall{}[b:B[a] {}\mrightarrow{} W(A;a.B[a])]. (Wsup(a;b) \mmember{} W(A;a.B[a]))
Date html generated:
2016_05_14-AM-06_15_28
Last ObjectModification:
2015_12_26-PM-00_04_57
Theory : co-recursion
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