Nuprl Lemma : W-rel_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[w:W(A;a.B[a])].
(W-rel(A;a.B[a];w) ∈ n:ℕ ⟶ (ℕn ⟶ cw-step(A;a.B[a])) ⟶ cw-step(A;a.B[a]) ⟶ ℙ)
Proof
Definitions occuring in Statement :
W-rel: W-rel(A;a.B[a];w),
W: W(A;a.B[a]),
cw-step: cw-step(A;a.B[a]),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
W-rel: W-rel(A;a.B[a];w),
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],
W: W(A;a.B[a]),
subtype_rel: A ⊆r B,
cw-step: cw-step(A;a.B[a]),
nat: ℕ,
prop: ℙ
Lemmas referenced :
param-W-rel_wf,
unit_wf2,
it_wf,
nat_wf,
int_seg_wf,
pcw-step_wf,
W_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
functionEquality,
cumulativity,
natural_numberEquality,
setElimination,
rename,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:W(A;a.B[a])].
(W-rel(A;a.B[a];w) \mmember{} n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} cw-step(A;a.B[a])) {}\mrightarrow{} cw-step(A;a.B[a]) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_15_02
Last ObjectModification:
2015_12_26-PM-00_05_13
Theory : co-recursion
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