Nuprl Lemma : int_trichot
∀i,j:ℤ. (i < j ∨ (i = j ∈ ℤ) ∨ (i > j))
Proof
Definitions occuring in Statement :
less_than: a < b,
gt: i > j,
all: ∀x:A. B[x],
or: P ∨ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
gt: i > j,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
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,
top: Top,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_or_lemma,
int_formula_prop_not_lemma,
intformeq_wf,
itermVar_wf,
intformless_wf,
intformor_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
decidable__lt,
equal_wf,
or_wf,
less_than_wf,
decidable__or
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll
Latex:
\mforall{}i,j:\mBbbZ{}. (i < j \mvee{} (i = j) \mvee{} (i > j))
Date html generated:
2016_05_14-AM-07_20_17
Last ObjectModification:
2016_01_07-PM-03_59_50
Theory : int_2
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