Nuprl Lemma : reject_cons_tl_sq

`∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ].  ([a / as]\[i] ~ [a / as\[i - 1]]) 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` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` 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` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` prop: `ℙ` bfalse: `ff` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{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_int_wf bool_wf eqtt_to_assert assert_of_le_int reduce_tl_cons_lemma satisfiable-full-omega-tt intformand_wf intformle_wf itermVar_wf itermConstant_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf list_ind_cons_lemma length_wf less_than_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality natural_numberEquality hypothesis lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality independent_pairFormation computeAll promote_hyp instantiate cumulativity independent_functionElimination because_Cache sqequalAxiom universeEquality

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

Date html generated: 2017_04_17-AM-08_48_39
Last ObjectModification: 2017_02_27-PM-05_05_59

Theory : list_1

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