Nuprl Lemma : radd-rminus
∀[x:ℝ]. ((x + -(x)) = r0)
Proof
Definitions occuring in Statement :
req: x = y,
rminus: -(x),
radd: a + b,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
radd: a + b,
implies: P ⇒ Q,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top,
real: ℝ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int-to-real: r(n),
rminus: -(x),
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
false: False,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s],
absval: |i|,
subtract: n - m
Lemmas referenced :
add-mul-special,
add-zero,
zero-mul,
zero-add,
mul-commutes,
mul-associates,
minus-one-mul,
add-associates,
subtract_wf,
absval_wf,
all_wf,
le_wf,
false_wf,
l_sum_nil_lemma,
l_sum_cons_lemma,
map_nil_lemma,
map_cons_lemma,
bdd-diff_weakening,
accelerate-bdd-diff,
bdd-diff_functionality,
iff_weakening_equal,
reg-seq-list-add-as-l_sum,
true_wf,
squash_wf,
bdd-diff_wf,
length_wf,
regular-int-seq_wf,
nat_plus_wf,
length_of_nil_lemma,
length_of_cons_lemma,
nil_wf,
cons_wf,
reg-seq-list-add_wf,
less_than_wf,
accelerate_wf,
real_wf,
req_witness,
int-to-real_wf,
rminus_wf,
radd_wf,
req-iff-bdd-diff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
dependent_set_memberEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
baseClosed,
because_Cache,
applyEquality,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality,
functionEquality,
intEquality,
setElimination,
rename,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_pairFormation,
lambdaFormation,
addEquality,
minusEquality,
multiplyEquality
Latex:
\mforall{}[x:\mBbbR{}]. ((x + -(x)) = r0)
Date html generated:
2016_05_18-AM-06_51_46
Last ObjectModification:
2016_01_17-AM-01_46_34
Theory : reals
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