### Nuprl Lemma : mklist-eq

`∀[n:ℕ]. ∀[f,g:ℕ ⟶ Base].  mklist(n;f) ~ mklist(n;g) supposing ∀[i:ℕn]. (f i ~ g i)`

Proof

Definitions occuring in Statement :  mklist: `mklist(n;f)` int_seg: `{i..j-}` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` apply: `f a` function: `x:A ⟶ B[x]` natural_number: `\$n` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` le: `A ≤ B` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` guard: `{T}` so_apply: `x[s]` mklist: `mklist(n;f)` less_than': `less_than'(a;b)` decidable: `Dec(P)` or: `P ∨ Q` sq_type: `SQType(T)` int_seg: `{i..j-}` lelt: `i ≤ j < k` uiff: `uiff(P;Q)` subtract: `n - m` less_than: `a < b`
Lemmas referenced :  int_seg_properties add-member-int_seg1 add-member-int_seg2 lelt_wf subtype_rel_self mklist-prepend1 le_wf int_term_value_add_lemma int_formula_prop_eq_lemma itermAdd_wf intformeq_wf decidable__equal_int int_subtype_base subtype_base_sq int_term_value_subtract_lemma int_formula_prop_not_lemma itermSubtract_wf intformnot_wf subtract_wf decidable__le false_wf int_seg_subtype_nat primrec0_lemma base_wf nat_wf less_than_irreflexivity less_than_transitivity1 sqequal-wf-base int_seg_wf uall_wf less_than_wf ge_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt nat_properties
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom productElimination applyEquality because_Cache functionEquality sqequalIntensionalEquality unionElimination instantiate equalityTransitivity equalitySymmetry dependent_set_memberEquality cumulativity addEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f,g:\mBbbN{}  {}\mrightarrow{}  Base].    mklist(n;f)  \msim{}  mklist(n;g)  supposing  \mforall{}[i:\mBbbN{}n].  (f  i  \msim{}  g  i)

Date html generated: 2016_05_14-PM-01_45_38
Last ObjectModification: 2016_01_15-AM-08_22_29

Theory : list_1

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