Nuprl Lemma : fset-closure-unique
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[r:T ⟶ ℕ]. ∀[fs:(T ⟶ T) List]. ∀[s,c1,c2:fset(T)].
(c1 = c2 ∈ fset(T)) supposing ((c2 = fs closure of s) and (c1 = fs closure of s))
Proof
Definitions occuring in Statement :
fset-closure: (c = fs closure of s),
fset: fset(T),
list: T List,
deq: EqDecider(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
guard: {T},
fset-closure: (c = fs closure of s),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
f-subset_antisymmetry,
fset-closure_wf,
fset_wf,
list_wf,
nat_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
productElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[r:T {}\mrightarrow{} \mBbbN{}]. \mforall{}[fs:(T {}\mrightarrow{} T) List]. \mforall{}[s,c1,c2:fset(T)].
(c1 = c2) supposing ((c2 = fs closure of s) and (c1 = fs closure of s))
Date html generated:
2016_05_14-PM-03_45_33
Last ObjectModification:
2015_12_26-PM-06_37_47
Theory : finite!sets
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