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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