### Nuprl Lemma : str-to-nat-plus-property

`∀[s:Atom List]. ∀[n:ℕ].  (str-to-nat-plus(s;n) = (str-to-nat(s) + (n * 10^||s||)) ∈ ℤ)`

Proof

Definitions occuring in Statement :  str-to-nat: `str-to-nat(s)` str-to-nat-plus: `str-to-nat-plus(s;n)` exp: `i^n` length: `||as||` list: `T List` nat: `ℕ` uall: `∀[x:A]. B[x]` multiply: `n * m` add: `n + m` natural_number: `\$n` int: `ℤ` atom: `Atom` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` implies: `P `` Q` str-to-nat: `str-to-nat(s)` str-to-nat-plus: `str-to-nat-plus(s;n)` all: `∀x:A. B[x]` so_lambda: `so_lambda(x,y,z.t[x; y; z])` top: `Top` so_apply: `x[s1;s2;s3]` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` prop: `ℙ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` guard: `{T}` uiff: `uiff(P;Q)` true: `True` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  list_induction uall_wf nat_wf equal_wf str-to-nat-plus_wf str-to-nat_wf exp_wf2 length_wf_nat list_wf list_ind_nil_lemma length_of_nil_lemma exp0_lemma nat_properties decidable__equal_int satisfiable-full-omega-tt intformnot_wf intformeq_wf itermVar_wf itermAdd_wf itermConstant_wf itermMultiply_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_formula_prop_wf list_ind_cons_lemma length_of_cons_lemma str1-to-nat_wf add_nat_wf multiply_nat_wf false_wf le_wf decidable__le add-is-int-iff intformand_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_le_lemma length_wf mul-swap add_functionality_wrt_eq non_neg_length exp_add iff_weakening_equal exp1 squash_wf true_wf mul-distributes-right mul-associates add-associates mul-commutes zero-mul zero-add add-swap add-commutes
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin extract_by_obid sqequalHypSubstitution isectElimination atomEquality sqequalRule lambdaEquality hypothesis intEquality hypothesisEquality applyEquality setElimination rename addEquality multiplyEquality natural_numberEquality independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality because_Cache unionElimination independent_isectElimination dependent_pairFormation int_eqEquality computeAll lambdaFormation axiomEquality dependent_set_memberEquality independent_pairFormation equalityTransitivity equalitySymmetry applyLambdaEquality pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed productElimination imageElimination imageMemberEquality universeEquality

Latex:
\mforall{}[s:Atom  List].  \mforall{}[n:\mBbbN{}].    (str-to-nat-plus(s;n)  =  (str-to-nat(s)  +  (n  *  10\^{}||s||)))

Date html generated: 2017_04_17-AM-09_18_09
Last ObjectModification: 2017_02_27-PM-05_22_19

Theory : decidable!equality

Home Index