### Nuprl Lemma : weakly-safe-seq_wf

`∀[R:ℕ ⟶ ℕ ⟶ ℙ]. ∀[n:ℕ]. ∀[s:ℕn ⟶ ℕ].  (weakly-safe-seq(R;n;s) ∈ ℙ)`

Proof

Definitions occuring in Statement :  weakly-safe-seq: `weakly-safe-seq(R;n;s)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` weakly-safe-seq: `weakly-safe-seq(R;n;s)` so_lambda: `λ2x.t[x]` nat: `ℕ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` sq_stable: `SqStable(P)` squash: `↓T` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` so_apply: `x[s]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin lambdaEquality hypothesisEquality dependent_set_memberEquality addEquality setElimination rename natural_numberEquality dependent_functionElimination hypothesis unionElimination independent_pairFormation lambdaFormation voidElimination productElimination independent_functionElimination independent_isectElimination imageMemberEquality baseClosed imageElimination applyEquality isect_memberEquality voidEquality intEquality because_Cache minusEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality

Latex:
\mforall{}[R:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}].    (weakly-safe-seq(R;n;s)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_13-PM-03_50_33
Last ObjectModification: 2016_01_14-PM-06_59_43

Theory : bar-induction

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