Nuprl Lemma : fixpoint-induction

[T:Type]. (∀f:bar(T) ⟶ bar(T). (fix(f) ∈ bar(T))) supposing (mono(T) and value-type(T))


Definitions occuring in Statement :  bar: bar(T) mono: mono(T) value-type: value-type(T) uimplies: 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: supposing a all: x:A. B[x] so_lambda: λ2x.t[x] so_apply: x[s] prop:
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

\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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