Nuprl Lemma : rmul_comm
∀[a,b:ℝ]. ((a * b) = (b * a))
Proof
Definitions occuring in Statement :
req: x = y,
rmul: a * b,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
real: ℝ,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
req-iff-bdd-diff,
rmul_wf,
req_witness,
real_wf,
reg-seq-mul_wf,
bdd-diff_weakening,
equal_wf,
squash_wf,
true_wf,
nat_plus_wf,
reg-seq-mul-comm,
iff_weakening_equal,
bdd-diff_functionality,
rmul-bdd-diff-reg-seq-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
applyEquality,
lambdaEquality,
setElimination,
rename,
dependent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionEquality,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[a,b:\mBbbR{}]. ((a * b) = (b * a))
Date html generated:
2017_10_02-PM-07_15_36
Last ObjectModification:
2017_07_28-AM-07_20_34
Theory : reals
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