Nuprl Lemma : es-interval-iseg
∀es:EO. ∀e3,e2,e1:E. (e1 ≤loc e2 ⇒ e1 ≤loc e3 ⇒ ([e1, e2] ≤ [e1, e3] ⇐⇒ e2 ≤loc e3 ))
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
or: P ∨ Q,
cand: A c∧ B,
uimplies: b supposing a,
es-le: e ≤loc e' ,
not: ¬A,
false: False
Latex:
\mforall{}es:EO. \mforall{}e3,e2,e1:E. (e1 \mleq{}loc e2 {}\mRightarrow{} e1 \mleq{}loc e3 {}\mRightarrow{} ([e1, e2] \mleq{} [e1, e3] \mLeftarrow{}{}\mRightarrow{} e2 \mleq{}loc e3 ))
Date html generated:
2016_05_16-AM-09_33_45
Last ObjectModification:
2015_12_28-PM-09_48_22
Theory : new!event-ordering
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