Nuprl Lemma : causal-pred-wellfounded
∀es:EO. ∀p:E ⟶ (E + Top). (causal-predecessor(es;p) ⇒ SWellFounded(p-graph(E;p) y x))
Proof
Definitions occuring in Statement :
causal-predecessor: causal-predecessor(es;p),
es-E: E,
event_ordering: EO,
strongwellfounded: SWellFounded(R[x; y]),
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
p-graph: p-graph(A;f)
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
p-graph: p-graph(A;f),
rel_implies: R1 => R2,
infix_ap: x f y,
causal-predecessor: causal-predecessor(es;p),
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
guard: {T},
and: P ∧ Q
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} SWellFounded(p-graph(E;p) y x))
Date html generated:
2016_05_16-AM-10_28_38
Last ObjectModification:
2015_12_28-PM-09_16_44
Theory : new!event-ordering
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