Nuprl Lemma : fixpoint-induction-bottom-bar

[E,S:Type].  (∀[G:S ⟶ bar(E)]. ∀[g:S ⟶ S].  (G[fix(g)] ∈ bar(E))) supposing ((⊥ ∈ S) and mono(E) and value-type(E))


Definitions occuring in Statement :  bar: bar(T) mono: mono(T) bottom: value-type: value-type(T) uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] member: t ∈ T fix: fix(F) function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  bar: bar(T) so_apply: x[s] member: t ∈ T uall: [x:A]. B[x] uimplies: supposing a
Lemmas referenced :  fixpoint-induction-bottom
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep sqequalHypSubstitution hypothesis

    (\mforall{}[G:S  {}\mrightarrow{}  bar(E)].  \mforall{}[g:S  {}\mrightarrow{}  S].    (G[fix(g)]  \mmember{}  bar(E)))  supposing 
          ((\mbot{}  \mmember{}  S)  and 
          mono(E)  and 

Date html generated: 2016_05_15-PM-10_04_45
Last ObjectModification: 2016_01_05-PM-06_48_38

Theory : bar!type

Home Index