Nuprl Lemma : radd-ac
∀[a,b,c:ℝ]. ((a + b + c) = (b + a + c))
Proof
Definitions occuring in Statement :
req: x = y,
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
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
Lemmas referenced :
req_witness,
radd_assoc,
iff_weakening_equal,
radd_comm_eq,
radd_wf,
real_wf,
true_wf,
squash_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[a,b,c:\mBbbR{}]. ((a + b + c) = (b + a + c))
Date html generated:
2016_05_18-AM-06_51_23
Last ObjectModification:
2016_01_17-AM-01_46_12
Theory : reals
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