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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
System: System(P.M[P]),
sub-system: sub-system(P.M[P];S1;S2),
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
ldag: LabeledDAG(T),
guard: {T}
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:
2016_05_17-AM-11_03_44
Last ObjectModification:
2015_12_29-PM-05_17_32
Theory : process-model
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