Nuprl Lemma : es-causle_weakening_p-le
∀es:EO. ∀p:E ⟶ (E + Top). (causal-predecessor(es;p) ⇒ (∀e,e':E. (e p≤ e' ⇒ e c≤ e')))
Proof
Definitions occuring in Statement :
es-p-le: e p≤ e',
causal-predecessor: causal-predecessor(es;p),
es-causle: e c≤ e',
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
es-p-le: e p≤ e',
or: P ∨ Q,
es-causle: e c≤ e',
member: t ∈ T,
guard: {T},
prop: ℙ,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e':E. (e p\mleq{} e' {}\mRightarrow{} e c\mleq{} e')))
Date html generated:
2016_05_16-AM-10_31_39
Last ObjectModification:
2016_01_06-PM-02_27_41
Theory : new!event-ordering
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