Nuprl Lemma : p-fun-exp_wf
∀[A:Type]. ∀[f:A ⟶ (A + Top)]. ∀[n:ℕ]. (f^n ∈ A ⟶ (A + Top))
Proof
Definitions occuring in Statement :
p-fun-exp: f^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
p-fun-exp: f^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ
Lemmas referenced :
primrec_wf,
top_wf,
p-id_wf,
p-compose_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
unionEquality,
hypothesis,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} (A + Top)]. \mforall{}[n:\mBbbN{}]. (f\^{}n \mmember{} A {}\mrightarrow{} (A + Top))
Date html generated:
2016_05_15-PM-03_31_44
Last ObjectModification:
2015_12_27-PM-01_11_21
Theory : general
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