Nuprl Lemma : radd_comm
∀[a,b:ℝ]. ((a + b) = (b + a))
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 :
equal_wf,
squash_wf,
true_wf,
real_wf,
radd_comm_eq,
radd_wf,
iff_weakening_equal,
req_weakening,
req_wf,
req_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
hyp_replacement,
applyLambdaEquality,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbR{}]. ((a + b) = (b + a))
Date html generated:
2017_10_02-PM-07_15_28
Last ObjectModification:
2017_07_28-AM-07_20_31
Theory : reals
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