Nuprl Lemma : fpf-all-empty
∀[A:Type]. ∀eq,P:Top. (∀y∈dom(⊗). w=⊗(y) ⇒ P[y;w] ⇐⇒ True)
Proof
Definitions occuring in Statement :
fpf-all: ∀x∈dom(f). v=f(x) ⇒ P[x; v],
fpf-empty: ⊗,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
fpf-empty: ⊗,
fpf-all: ∀x∈dom(f). v=f(x) ⇒ P[x; v],
member: t ∈ T,
top: Top,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
so_lambda: λ2x.t[x],
prop: ℙ,
false: False,
so_apply: x[s],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q
Latex:
\mforall{}[A:Type]. \mforall{}eq,P:Top. (\mforall{}y\mmember{}dom(\motimes{}). w=\motimes{}(y) {}\mRightarrow{} P[y;w] \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_16-AM-11_31_26
Last ObjectModification:
2015_12_29-AM-09_27_04
Theory : event-ordering
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