Nuprl Lemma : radd_comm_eq
∀[a,b:ℝ]. ((a + b) = (b + a) ∈ ℝ)
Proof
Definitions occuring in Statement :
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
true: True,
uimplies: b supposing a,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
radd-list_functionality_wrt_permutation,
cons_wf,
real_wf,
nil_wf,
permutation-swap-first2,
equal_wf,
squash_wf,
true_wf,
radd-as-radd-list,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
because_Cache,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
natural_numberEquality,
extract_by_obid,
independent_isectElimination,
dependent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[a,b:\mBbbR{}]. ((a + b) = (b + a))
Date html generated:
2017_10_02-PM-07_15_26
Last ObjectModification:
2017_07_28-AM-07_20_29
Theory : reals
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