Nuprl Lemma : retraction_wf
∀[T:Type]. ∀[f:T ⟶ T]. (retraction(T;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
retraction: retraction(T;f),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
retraction: retraction(T;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
all_wf,
or_wf,
equal_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} T]. (retraction(T;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-05_05_31
Last ObjectModification:
2015_12_27-PM-02_26_35
Theory : general
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