Nuprl Lemma : right_mul_preserves_le
∀[a,b:ℤ]. ∀[n:ℕ]. (a * n) ≤ (b * n) supposing a ≤ b
Proof
Definitions occuring in Statement :
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
prop: ℙ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermMultiply_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
nat_wf,
le_wf,
less_than'_wf,
mul_preserves_le
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
voidElimination,
multiplyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[a,b:\mBbbZ{}]. \mforall{}[n:\mBbbN{}]. (a * n) \mleq{} (b * n) supposing a \mleq{} b
Date html generated:
2016_05_14-AM-07_20_32
Last ObjectModification:
2016_01_07-PM-03_59_48
Theory : int_2
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