Nuprl Lemma : rless-property
∀x,y:ℝ. ∀n:x < y. (x n) + 4 < y n
Proof
Definitions occuring in Statement :
rless: x < y,
real: ℝ,
less_than: a < b,
all: ∀x:A. B[x],
apply: f a,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
rless: x < y,
sq_exists: ∃x:{A| B[x]},
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
real: ℝ,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
top: Top
Lemmas referenced :
real_wf,
rless_wf,
false_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
add-is-int-iff,
less_than_wf,
decidable__lt,
nat_plus_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
addEquality,
applyEquality,
dependent_set_memberEquality,
natural_numberEquality,
because_Cache,
unionElimination,
imageElimination,
productElimination,
pointwiseFunctionality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}x,y:\mBbbR{}. \mforall{}n:x < y. (x n) + 4 < y n
Date html generated:
2016_05_18-AM-07_31_55
Last ObjectModification:
2016_01_17-AM-02_00_19
Theory : reals
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