### Nuprl Lemma : exp-zero

`∀[n:ℕ+]. (0^n = 0 ∈ ℤ)`

Proof

Definitions occuring in Statement :  exp: `i^n` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` squash: `↓T` prop: `ℙ` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` all: `∀x:A. B[x]` nat_plus: `ℕ+` so_lambda: `λ2x.t[x]` so_apply: `x[s]` exp: `i^n` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` bfalse: `ff` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` nequal: `a ≠ b ∈ T ` subtract: `n - m` nat: `ℕ` decidable: `Dec(P)`
Lemmas referenced :  equal_wf squash_wf true_wf exp1 iff_weakening_equal nat_plus_properties equal-wf-base int_subtype_base nat_plus_wf primrec-wf-nat-plus equal-wf-T-base exp_wf2 nat_plus_subtype_nat primrec-unroll eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int satisfiable-full-omega-tt intformand_wf intformeq_wf itermVar_wf itermConstant_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int itermAdd_wf int_term_value_add_lemma add-associates zero-mul primrec_wf decidable__le intformnot_wf intformle_wf int_formula_prop_not_lemma int_formula_prop_le_lemma le_wf int_seg_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination introduction extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry because_Cache intEquality natural_numberEquality sqequalRule imageMemberEquality baseClosed universeEquality independent_isectElimination productElimination independent_functionElimination lambdaFormation rename setElimination baseApply closedConclusion addEquality isect_memberEquality voidElimination voidEquality unionElimination equalityElimination dependent_pairFormation int_eqEquality dependent_functionElimination independent_pairFormation computeAll promote_hyp instantiate cumulativity minusEquality dependent_set_memberEquality multiplyEquality

Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  (0\^{}n  =  0)

Date html generated: 2017_04_17-AM-09_44_52
Last ObjectModification: 2017_02_27-PM-05_38_58

Theory : num_thy_1

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