Nuprl Lemma : es-base-pred-less
∀es:EO. ∀e:es-base-E(es). ((¬↑(es-eq(es) pred1(e) e)) ⇒ (pred1(e) < e))
Proof
Definitions occuring in Statement :
es-eq: es-eq(es),
es-causl: (e < e'),
es-base-pred: pred1(e),
es-base-E: es-base-E(es),
event_ordering: EO,
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
deq: EqDecider(T),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a
Latex:
\mforall{}es:EO. \mforall{}e:es-base-E(es). ((\mneg{}\muparrow{}(es-eq(es) pred1(e) e)) {}\mRightarrow{} (pred1(e) < e))
Date html generated:
2016_05_16-AM-09_15_53
Last ObjectModification:
2015_12_28-PM-09_57_26
Theory : new!event-ordering
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