Nuprl Lemma : radd-rminus-both
∀[x:ℝ]. (((x + -(x)) = r0) ∧ ((-(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],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
radd_wf,
req_witness,
iff_weakening_equal,
int-to-real_wf,
rminus_wf,
radd_comm_eq,
real_wf,
true_wf,
squash_wf,
req_wf,
radd-rminus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairEquality,
because_Cache
Latex:
\mforall{}[x:\mBbbR{}]. (((x + -(x)) = r0) \mwedge{} ((-(x) + x) = r0))
Date html generated:
2016_05_18-AM-06_51_48
Last ObjectModification:
2016_01_17-AM-01_46_30
Theory : reals
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