Nuprl Lemma : causal_order_wf
∀[T:Type]. ∀[L:T List]. ∀[P,Q:ℕ||L|| ⟶ ℙ]. ∀[R:ℕ||L|| ⟶ ℕ||L|| ⟶ ℙ]. (causal_order(L;R;P;Q) ∈ ℙ)
Proof
Definitions occuring in Statement :
causal_order: causal_order(L;R;P;Q),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
causal_order: causal_order(L;R;P;Q),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
length_wf,
exists_wf,
le_wf,
subtype_rel_self,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
productEquality,
setElimination,
rename,
instantiate,
universeEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
inhabitedIsType,
isect_memberEquality,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P,Q:\mBbbN{}||L|| {}\mrightarrow{} \mBbbP{}]. \mforall{}[R:\mBbbN{}||L|| {}\mrightarrow{} \mBbbN{}||L|| {}\mrightarrow{} \mBbbP{}]. (causal\_order(L;R;P;Q) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_57_31
Last ObjectModification:
2018_09_27-AM-09_37_30
Theory : list!
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