Nuprl Lemma : lt_to_le
∀[i,j:ℤ]. uiff(i < j;(i + 1) ≤ j)
Proof
Definitions occuring in Statement :
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B
Lemmas referenced :
member-less_than,
le_wf,
decidable__lt,
less_than_wf,
less_than'_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
addEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
productElimination,
independent_pairEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[i,j:\mBbbZ{}]. uiff(i < j;(i + 1) \mleq{} j)
Date html generated:
2016_05_14-AM-07_20_19
Last ObjectModification:
2016_01_07-PM-03_59_51
Theory : int_2
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