Nuprl Lemma : system-equiv_wf
∀[M:Type ⟶ Type]. ∀[S1,S2:System(P.M[P])]. (system-equiv(P.M[P];S1;S2) ∈ ℙ) supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
component: component(P.M[P])
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[S1,S2:System(P.M[P])]. (system-equiv(P.M[P];S1;S2) \mmember{} \mBbbP{}) supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_37_01
Last ObjectModification:
2016_01_18-AM-00_18_17
Theory : process-model
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