Nuprl Lemma : eo-record-record-eq
∀r:eo_record{i:l}(). ∀r':record(x.eo-record-type{i:l}(r) x).
((r' = r ∈ record(x.eo-record-type{i:l}(r) x)) ⇒ (r' = r ∈ eo_record{i:l}()))
Proof
Definitions occuring in Statement :
eo-record-type: eo-record-type{i:l}(r),
eo_record: eo_record{i:l}(),
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
equal: s = t ∈ T,
record: record(x.T[x])
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
eo_record: eo_record{i:l}(),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
record: record(x.T[x]),
eo-record-type: eo-record-type{i:l}(r),
top: Top,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q
Latex:
\mforall{}r:eo\_record\{i:l\}(). \mforall{}r':record(x.eo-record-type\{i:l\}(r) x). ((r' = r) {}\mRightarrow{} (r' = r))
Date html generated:
2016_05_16-AM-09_13_27
Last ObjectModification:
2015_12_28-PM-09_59_57
Theory : new!event-ordering
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