Nuprl Lemma : W-type_wf
∀[A:Type]. ∀[B:A ⟶ Type]. (W-type(A; a.B[a]) ∈ Type)
Proof
Definitions occuring in Statement :
W-type: W-type(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,
W-type: W-type(A; a.B[a]),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
co-W_wf,
all_wf,
nat_wf,
unit_wf2,
W-bars_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
unionEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (W-type(A; a.B[a]) \mmember{} Type)
Date html generated:
2016_05_15-PM-10_06_50
Last ObjectModification:
2015_12_27-PM-05_50_23
Theory : bar!induction
Home
Index