### Nuprl Lemma : div_one

`∀[x:ℤ]. (x ÷ 1 ~ x)`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` divide: `n ÷ m` natural_number: `\$n` int: `ℤ` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` sq_type: `SQType(T)` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` int_nzero: `ℤ-o` true: `True` nequal: `a ≠ b ∈ T ` not: `¬A` false: `False` prop: `ℙ` exists: `∃x:A. B[x]` and: `P ∧ Q` cand: `A c∧ B` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` absval: `|i|` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` le: `A ≤ B` subtype_rel: `A ⊆r B` nat: `ℕ` uiff: `uiff(P;Q)`
Lemmas referenced :  subtype_base_sq int_subtype_base istype-int nequal_wf decidable__equal_int full-omega-unsat intformnot_wf intformeq_wf itermVar_wf itermAdd_wf itermMultiply_wf itermConstant_wf int_formula_prop_not_lemma istype-void int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_mul_lemma int_term_value_constant_lemma int_formula_prop_wf istype-false istype-le istype-less_than absval_wf intformand_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_less_lemma div_unique3
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut thin instantiate extract_by_obid sqequalHypSubstitution isectElimination cumulativity intEquality independent_isectElimination hypothesis dependent_functionElimination equalityTransitivity equalitySymmetry hypothesisEquality independent_functionElimination axiomSqEquality dependent_set_memberEquality_alt natural_numberEquality lambdaFormation_alt voidElimination equalityIstype inhabitedIsType baseClosed sqequalBase universeIsType dependent_pairFormation_alt sqequalRule independent_pairFormation minusEquality because_Cache imageMemberEquality unionElimination approximateComputation lambdaEquality_alt int_eqEquality isect_memberEquality_alt imageElimination productElimination productIsType applyEquality setElimination rename baseApply closedConclusion functionIsType

Latex:
\mforall{}[x:\mBbbZ{}].  (x  \mdiv{}  1  \msim{}  x)

Date html generated: 2020_05_19-PM-09_41_18
Last ObjectModification: 2019_10_16-PM-04_23_57

Theory : int_2

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