Nuprl Lemma : sub-system_transitivity
∀[M:Type ─→ Type]
∀S1,S2,S3:System(P.M[P]). (sub-system(P.M[P];S1;S2) ⇒ sub-system(P.M[P];S2;S3) ⇒ sub-system(P.M[P];S1;S3))
Proof
Definitions occuring in Statement :
sub-system: sub-system(P.M[P];S1;S2),
System: System(P.M[P]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
sublist_transitivity,
lg-contains_transitivity,
sublist_wf,
component_wf,
lg-contains_wf,
pInTransit_wf,
System_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}S1,S2,S3:System(P.M[P]).
(sub-system(P.M[P];S1;S2) {}\mRightarrow{} sub-system(P.M[P];S2;S3) {}\mRightarrow{} sub-system(P.M[P];S1;S3))
Date html generated:
2015_07_23-AM-11_19_39
Last ObjectModification:
2015_01_28-PM-11_17_29
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