### Nuprl Lemma : step-function_wf

`∀[T:Type]. ∀[transition:T ⟶ T ⟶ ℙ]. ∀[X:Type].  (step-function(T;transition;X) ∈ Type)`

Proof

Definitions occuring in Statement :  step-function: `step-function(T;transition;X)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` step-function: `step-function(T;transition;X)` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` so_apply: `x[s]` exists: `∃x:A. B[x]` prop: `ℙ`
Lemmas referenced :  exists_wf isect2_wf isect2_subtype_rel
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule setEquality hypothesisEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality applyEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality isect_memberEquality because_Cache functionEquality cumulativity

Latex:
\mforall{}[T:Type].  \mforall{}[transition:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[X:Type].    (step-function(T;transition;X)  \mmember{}  Type)

Date html generated: 2016_05_15-PM-10_11_38
Last ObjectModification: 2015_12_27-PM-05_58_22

Theory : eval!all

Home Index