### 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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