Nuprl Lemma : fpf-rename-dom2
∀[A,C:Type]. ∀[eqa:EqDecider(A)]. ∀[eqc:EqDecider(C)]. ∀[eqc':Top]. ∀[r:A ⟶ C]. ∀[f:a:A fp-> Top]. ∀[a:A].
{↑r a ∈ dom(rename(r;f)) supposing ↑a ∈ dom(f)}
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
fpf-rename: rename(r;f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
pi1: fst(t),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Latex:
\mforall{}[A,C:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc:EqDecider(C)]. \mforall{}[eqc':Top]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> Top].
\mforall{}[a:A].
\{\muparrow{}r a \mmember{} dom(rename(r;f)) supposing \muparrow{}a \mmember{} dom(f)\}
Date html generated:
2016_05_16-AM-11_25_45
Last ObjectModification:
2015_12_29-AM-09_22_51
Theory : event-ordering
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