Nuprl Lemma : fixpoint-induction
∀[T:Type]. (∀f:bar(T) ⟶ bar(T). (fix(f) ∈ bar(T))) supposing (mono(T) and value-type(T))
Proof
Definitions occuring in Statement :
bar: bar(T),
mono: mono(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
fix: fix(F),
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
fixpoint-induction-bottom-bar,
mono_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. (\mforall{}f:bar(T) {}\mrightarrow{} bar(T). (fix(f) \mmember{} bar(T))) supposing (mono(T) and value-type(T))
Date html generated:
2016_05_15-PM-10_04_46
Last ObjectModification:
2015_12_27-PM-05_16_45
Theory : bar!type
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