### Nuprl Lemma : weak-TI_wf

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

Proof

Definitions occuring in Statement :  weak-TI: `weak-TI(T;x,y.R[x; y];t.Q[t])` uall: `∀[x:A]. B[x]` prop: `ℙ` 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` weak-TI: `weak-TI(T;x,y.R[x; y];t.Q[t])` implies: `P `` Q` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` so_apply: `x[s]`
Lemmas referenced :  all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule functionEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

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

Date html generated: 2016_05_13-PM-03_50_01
Last ObjectModification: 2015_12_26-AM-10_17_34

Theory : bar-induction

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