Nuprl Lemma : seq-normalize-equal

`∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T].  (seq-normalize(n;s) = s ∈ (ℕn ⟶ T))`

Proof

Definitions occuring in Statement :  seq-normalize: `seq-normalize(n;s)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` seq-normalize: `seq-normalize(n;s)` int_seg: `{i..j-}` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` lelt: `i ≤ j < k`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf int_seg_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base iff_transitivity assert_wf bnot_wf not_wf iff_weakening_uiff assert_of_bnot nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut functionExtensionality sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality natural_numberEquality imageMemberEquality baseClosed imageElimination independent_functionElimination applyEquality dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity impliesFunctionality functionEquality axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:\mBbbN{}n  {}\mrightarrow{}  T].    (seq-normalize(n;s)  =  s)

Date html generated: 2017_04_14-AM-07_26_40
Last ObjectModification: 2017_02_27-PM-02_56_02

Theory : bar-induction

Home Index