Nuprl Lemma : le_to_lt
∀[i,j:ℤ]. uiff(i ≤ j;i < j + 1)
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 :
le: A ≤ B,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
member-less_than,
less_than_wf,
less_than'_wf,
decidable__le,
le_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__lt
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
because_Cache,
axiomEquality,
independent_pairEquality,
productElimination,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
isectElimination,
unionElimination,
hypothesis,
natural_numberEquality,
addEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[i,j:\mBbbZ{}]. uiff(i \mleq{} j;i < j + 1)
Date html generated:
2018_05_21-PM-00_25_44
Last ObjectModification:
2018_05_15-PM-04_42_51
Theory : int_2
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