Nuprl Lemma : es-open-interval-closed
∀[es:EO]. ∀[e1,e2:E]. (pred(e1), e2) = [e1;e2) ∈ (E List) supposing ¬↑first(e1)
Proof
Definitions occuring in Statement :
es-closed-open-interval: [e;e'),
es-open-interval: (e, e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-closed-open-interval: [e;e'),
es-open-interval: (e, e'),
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
es-locl: (e <loc e'),
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
guard: {T},
true: True
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. (pred(e1), e2) = [e1;e2) supposing \mneg{}\muparrow{}first(e1)
Date html generated:
2016_05_16-AM-09_36_54
Last ObjectModification:
2016_01_17-PM-01_27_40
Theory : new!event-ordering
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