Nuprl Lemma : trivial-rless-radd
∀a,d:ℝ. (uiff(a < (a + d);r0 < d) ∧ uiff(a < (d + a);r0 < d))
Proof
Definitions occuring in Statement :
rless: x < y,
radd: a + b,
int-to-real: r(n),
real: ℝ,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
itermConstant: "const",
req_int_terms: t1 ≡ t2,
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rless-implies-rless,
int-to-real_wf,
radd_wf,
real_term_polynomial,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_var_lemma,
req-iff-rsub-is-0,
rsub_wf,
rless_wf,
squash_wf,
true_wf,
real_wf,
radd_comm_eq,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
independent_pairFormation,
isect_memberFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
computeAll,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination
Latex:
\mforall{}a,d:\mBbbR{}. (uiff(a < (a + d);r0 < d) \mwedge{} uiff(a < (d + a);r0 < d))
Date html generated:
2017_10_03-AM-08_25_50
Last ObjectModification:
2017_07_28-AM-07_23_58
Theory : reals
Home
Index