### Nuprl Lemma : ext2Cantor_eq

`∀[s:𝔹 List]. ∀[d:𝔹].  (ext2Cantor(||s||;λx.s[x];d) = extl2Cantor(s;d) ∈ (ℕ ⟶ 𝔹))`

Proof

Definitions occuring in Statement :  extl2Cantor: `extl2Cantor(s;b)` ext2Cantor: `ext2Cantor(n;f;d)` select: `L[n]` length: `||as||` list: `T List` nat: `ℕ` bool: `𝔹` uall: `∀[x:A]. B[x]` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` extl2Cantor: `extl2Cantor(s;b)` ext2Cantor: `ext2Cantor(n;f;d)` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` bfalse: `ff`
Lemmas referenced :  lt_int_wf length_wf bool_wf eqtt_to_assert assert_of_lt_int select_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf equal_wf nat_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lambdaEquality extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination because_Cache dependent_functionElimination natural_numberEquality dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll equalityTransitivity equalitySymmetry independent_functionElimination axiomEquality

Latex:
\mforall{}[s:\mBbbB{}  List].  \mforall{}[d:\mBbbB{}].    (ext2Cantor(||s||;\mlambda{}x.s[x];d)  =  extl2Cantor(s;d))

Date html generated: 2017_04_17-AM-09_58_05
Last ObjectModification: 2017_02_27-PM-05_51_37

Theory : continuity

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