Nuprl Lemma : rminus_wf
∀[x:ℝ]. (-(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
rminus: -(x),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rminus: -(x),
real: ℝ,
prop: ℙ,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
squash: ↓T,
nat_plus: ℕ+,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
top: Top,
subtract: n - m
Lemmas referenced :
one-mul,
mul-associates,
mul-swap,
minus-minus,
minus-add,
add-commutes,
minus-one-mul,
mul-distributes,
iff_weakening_equal,
subtract_wf,
absval_sym,
true_wf,
squash_wf,
le_wf,
real_wf,
regular-int-seq_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
lambdaEquality,
minusEquality,
applyEquality,
hypothesisEquality,
lemma_by_obid,
hypothesis,
isectElimination,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
dependent_functionElimination,
imageElimination,
intEquality,
multiplyEquality,
addEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache
Latex:
\mforall{}[x:\mBbbR{}]. (-(x) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-06_48_47
Last ObjectModification:
2016_01_17-AM-01_45_35
Theory : reals
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