Nuprl Lemma : select-cons-tl

`∀[a,as:Top]. ∀[i:ℤ].  [a / as][i] ~ as[i - 1] supposing 0 < i`

Proof

Definitions occuring in Statement :  select: `L[n]` cons: `[a / b]` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` top: `Top` subtract: `n - m` natural_number: `\$n` int: `ℤ` sqequal: `s ~ t`
Definitions unfolded in proof :  select: `L[n]` all: `∀x:A. B[x]` so_lambda: `λ2x y.t[x; y]` member: `t ∈ T` top: `Top` so_apply: `x[s1;s2]` uall: `∀[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)` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` subtype_rel: `A ⊆r B` le: `A ≤ B` 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` has-value: `(a)↓`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin isect_memberEquality voidElimination voidEquality hypothesis isectElimination hypothesisEquality natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination lessCases isect_memberFormation sqequalAxiom because_Cache independent_pairFormation imageMemberEquality baseClosed imageElimination independent_functionElimination addEquality applyEquality lambdaEquality intEquality dependent_pairFormation promote_hyp instantiate cumulativity callbyvalueReduce

Latex:
\mforall{}[a,as:Top].  \mforall{}[i:\mBbbZ{}].    [a  /  as][i]  \msim{}  as[i  -  1]  supposing  0  <  i

Date html generated: 2017_04_14-AM-08_36_40
Last ObjectModification: 2017_02_27-PM-03_28_26

Theory : list_0

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