Nuprl Lemma : Q-R-glued-empty
∀[Info:Type]. ∀es:EO+(Info). ∀[Q,R:E ⟶ E ⟶ ℙ]. ∀[B:Type]. ∀f:Top. Empty:Q →─f⟶ Empty:R
Proof
Definitions occuring in Statement :
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb,
es-empty-interface: Empty,
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb,
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
es-E-interface: E(X),
member: t ∈ T,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
inject: Inj(A;B;f),
es-interface-predicate: {I},
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
weak-antecedent-surjection: Q ←←= f== P,
weak-antecedent-function: Q ←==f== P,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
es-E: E,
false: False,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
event_ordering: EO
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}[Q,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:Type]. \mforall{}f:Top. Empty:Q \mrightarrow{}{}f{}\mrightarrow{} Empty:R
Date html generated:
2016_05_17-AM-07_55_07
Last ObjectModification:
2016_01_17-PM-02_45_09
Theory : event-ordering
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