Nuprl Lemma : pcw-pp-null_wf
∀[P:Type]. ∀[A:P ⟶ Type]. ∀[B:p:P ⟶ A[p] ⟶ Type]. ∀[C:p:P ⟶ a:A[p] ⟶ B[p;a] ⟶ P]. ∀[pp:PartialPath].
(pcw-pp-null(pp) ∈ 𝔹)
Proof
Definitions occuring in Statement :
pcw-pp-null: pcw-pp-null(pp),
pcw-pp: PartialPath,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
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,
pcw-pp-null: pcw-pp-null(pp),
pcw-pp: PartialPath,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
le_int_wf,
pcw-pp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
lemma_by_obid,
isectElimination,
natural_numberEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
applyEquality,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:Type]. \mforall{}[A:P {}\mrightarrow{} Type]. \mforall{}[B:p:P {}\mrightarrow{} A[p] {}\mrightarrow{} Type]. \mforall{}[C:p:P {}\mrightarrow{} a:A[p] {}\mrightarrow{} B[p;a] {}\mrightarrow{} P].
\mforall{}[pp:PartialPath].
(pcw-pp-null(pp) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-AM-06_13_01
Last ObjectModification:
2015_12_26-PM-00_05_49
Theory : co-recursion
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