Nuprl Lemma : radd-preserves-req
∀[x,y,z:ℝ]. uiff(x = y;(z + x) = (z + y))
Proof
Definitions occuring in Statement :
req: x = y,
radd: a + b,
real: ℝ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real_wf,
req_wf,
req_witness,
req_weakening,
radd_functionality,
radd_wf,
req_functionality,
rminus_wf,
rmul_wf,
int-to-real_wf,
uiff_transitivity,
req_transitivity,
rminus-as-rmul,
radd-assoc,
req_inversion,
rmul-identity1,
rmul-distrib2,
rmul_functionality,
radd-int,
rmul-zero-both,
radd-zero-both
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_pairEquality,
sqequalRule,
independent_functionElimination,
productElimination,
independent_isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
minusEquality,
natural_numberEquality,
addEquality
Latex:
\mforall{}[x,y,z:\mBbbR{}]. uiff(x = y;(z + x) = (z + y))
Date html generated:
2017_10_02-PM-07_17_40
Last ObjectModification:
2017_07_28-AM-07_21_15
Theory : reals
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