Nuprl Lemma : Wsucc_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[w:W(A;a.B[a])]. (Wsucc(A;a.B[a];w) ∈ ℙ)
Proof
Definitions occuring in Statement :
Wsucc: Wsucc(A;a.B[a];w),
W: W(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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Wsucc: Wsucc(A;a.B[a];w),
so_apply: x[s],
so_lambda: λ2x.t[x],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
ext-eq_wf,
W-ext,
pi1_wf,
W_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
lambdaEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:W(A;a.B[a])]. (Wsucc(A;a.B[a];w) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_16_43
Last ObjectModification:
2015_12_26-PM-00_04_14
Theory : co-recursion
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