### Nuprl Lemma : int-minus-comparison_wf

`∀[T:Type]. ∀[f:T ⟶ ℤ].  (int-minus-comparison(f) ∈ comparison(T))`

Proof

Definitions occuring in Statement :  int-minus-comparison: `int-minus-comparison(f)` comparison: `comparison(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` int-minus-comparison: `int-minus-comparison(f)` comparison: `comparison(T)` and: `P ∧ Q` cand: `A c∧ B` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` uiff: `uiff(P;Q)` le: `A ≤ B` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  equal-wf-T-base all_wf le_wf int_formula_prop_le_lemma intformle_wf decidable__le equal_wf false_wf int_term_value_constant_lemma int_formula_prop_and_lemma itermConstant_wf intformand_wf subtract-is-int-iff int_formula_prop_wf int_term_value_minus_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma itermMinus_wf itermVar_wf itermSubtract_wf intformeq_wf intformnot_wf satisfiable-full-omega-tt decidable__equal_int subtract_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis sqequalRule lambdaFormation dependent_functionElimination because_Cache unionElimination natural_numberEquality independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll independent_pairFormation pointwiseFunctionality rename equalityTransitivity equalitySymmetry promote_hyp baseApply closedConclusion baseClosed productElimination productEquality cumulativity minusEquality functionEquality axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  \mBbbZ{}].    (int-minus-comparison(f)  \mmember{}  comparison(T))

Date html generated: 2016_05_14-PM-02_36_17
Last ObjectModification: 2016_01_15-AM-07_43_11

Theory : list_1

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