### Nuprl Lemma : reject_cons_tl

`∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ].`
`  ([a / as]\[i] = [a / as\[i - 1]] ∈ (T List)) supposing ((i ≤ ||as||) and 0 < i)`

Proof

Definitions occuring in Statement :  length: `||as||` reject: `as\[i]` cons: `[a / b]` list: `T List` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` subtract: `n - m` natural_number: `\$n` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ` reject: `as\[i]` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` top: `Top` le: `A ≤ B` false: `False` guard: `{T}` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]`
Lemmas referenced :  le_wf length_wf less_than_wf list_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int reduce_tl_cons_lemma less_than_transitivity1 less_than_irreflexivity eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot not_functionality_wrt_uiff assert_wf list_ind_cons_lemma cons_wf reject_wf subtract_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut hypothesis Error :universeIsType,  extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry natural_numberEquality because_Cache intEquality universeEquality lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination dependent_functionElimination voidElimination voidEquality independent_functionElimination dependent_pairFormation promote_hyp instantiate cumulativity

Latex:
\mforall{}[T:Type].  \mforall{}[a:T].  \mforall{}[as:T  List].  \mforall{}[i:\mBbbZ{}].
([a  /  as]\mbackslash{}[i]  =  [a  /  as\mbackslash{}[i  -  1]])  supposing  ((i  \mleq{}  ||as||)  and  0  <  i)

Date html generated: 2019_06_20-PM-00_40_17
Last ObjectModification: 2018_09_26-PM-02_47_36

Theory : list_0

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