### Nuprl Lemma : eq_ext2Cantor

`∀n:ℕ. ∀s:ℕn ⟶ 𝔹. ∀d1,d2:𝔹.  (ext2Cantor(n;s;d1) = ext2Cantor(n;s;d2) ∈ (ℕn ⟶ 𝔹))`

Proof

Definitions occuring in Statement :  ext2Cantor: `ext2Cantor(n;f;d)` int_seg: `{i..j-}` nat: `ℕ` bool: `𝔹` all: `∀x:A. B[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` ext2Cantor: `ext2Cantor(n;f;d)` uall: `∀[x:A]. B[x]` int_seg: `{i..j-}` nat: `ℕ` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` ge: `i ≥ j ` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int int_seg_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf int_seg_properties nat_properties satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_formula_prop_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut hypothesis because_Cache lambdaEquality introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality unionElimination equalityElimination productElimination independent_isectElimination sqequalRule applyEquality functionExtensionality natural_numberEquality dependent_pairFormation equalityTransitivity equalitySymmetry promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination int_eqEquality intEquality isect_memberEquality voidEquality independent_pairFormation computeAll

Latex:
\mforall{}n:\mBbbN{}.  \mforall{}s:\mBbbN{}n  {}\mrightarrow{}  \mBbbB{}.  \mforall{}d1,d2:\mBbbB{}.    (ext2Cantor(n;s;d1)  =  ext2Cantor(n;s;d2))

Date html generated: 2017_04_17-AM-09_57_45
Last ObjectModification: 2017_02_27-PM-05_51_05

Theory : continuity

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