Nuprl Lemma : uniform-TI_wf

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[Q:T ⟶ ℙ].  (uniform-TI(T;x,y.R[x;y];t.Q[t]) ∈ ℙ)


Proof




Definitions occuring in Statement :  uniform-TI: uniform-TI(T;x,y.R[x; y];t.Q[t]) uall: [x:A]. B[x] prop: so_apply: x[s1;s2] so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uniform-TI: uniform-TI(T;x,y.R[x; y];t.Q[t]) implies:  Q prop: so_lambda: λ2x.t[x] so_apply: x[s1;s2] subtype_rel: A ⊆B so_apply: x[s]
Lemmas referenced :  uall_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule functionEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality setEquality applyEquality hypothesis universeEquality setElimination rename because_Cache axiomEquality equalityTransitivity equalitySymmetry cumulativity isect_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[Q:T  {}\mrightarrow{}  \mBbbP{}].    (uniform-TI(T;x,y.R[x;y];t.Q[t])  \mmember{}  \mBbbP{})



Date html generated: 2016_05_13-PM-03_49_59
Last ObjectModification: 2015_12_26-AM-10_17_35

Theory : bar-induction


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