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: List nat: bool: 𝔹 uall: [x:A]. B[x] lambda: λx.A[x] function: x:A ⟶ B[x] equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T extl2Cantor: extl2Cantor(s;b) ext2Cantor: ext2Cantor(n;f;d) nat: all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt ifthenelse: if then else fi  uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a ge: i ≥  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: 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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