Nuprl Lemma : simple-comb-1-disjoint-classrel
∀[Info,T,A,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[f:A ⟶ T].
(disjoint-classrel(es;A;X;B;Y) ⇒ disjoint-classrel(es;T;lifting-1(f)|X|;B;Y))
Proof
Definitions occuring in Statement :
simple-comb-1: F|X|,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
lifting-1: lifting-1(f)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
all: ∀x:A. B[x],
member: t ∈ T,
or: P ∨ Q,
not: ¬A,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,T,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[f:A {}\mrightarrow{} T].
(disjoint-classrel(es;A;X;B;Y) {}\mRightarrow{} disjoint-classrel(es;T;lifting-1(f)|X|;B;Y))
Date html generated:
2016_05_17-AM-09_33_53
Last ObjectModification:
2015_12_29-PM-03_59_29
Theory : classrel!lemmas
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