Nuprl Lemma : es-le-first
∀[es:EO]. ∀[j,e:E]. if first(j) then j else e fi = e ∈ E supposing e ≤loc j
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-first: first(e),
es-E: E,
event_ordering: EO,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
es-E: E,
es-base-E: es-base-E(es),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-le: e ≤loc e' ,
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
false: False
Latex:
\mforall{}[es:EO]. \mforall{}[j,e:E]. if first(j) then j else e fi = e supposing e \mleq{}loc j
Date html generated:
2016_05_16-AM-09_18_36
Last ObjectModification:
2015_12_28-PM-09_56_24
Theory : new!event-ordering
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