Nuprl Lemma : req-implies-req
∀[a,b,c,d:ℝ]. (a = b) supposing ((c = d) and ((d - c) = (b - a)))
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q,
prop: ℙ,
rsub: x - y,
guard: {T}
Lemmas referenced :
radd-preserves-req,
rminus_wf,
radd-rminus-both,
req_witness,
req_wf,
rsub_wf,
real_wf,
radd_wf,
int-to-real_wf,
req_functionality,
req_weakening,
radd_comm,
req_inversion,
req_transitivity
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,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality
Latex:
\mforall{}[a,b,c,d:\mBbbR{}]. (a = b) supposing ((c = d) and ((d - c) = (b - a)))
Date html generated:
2017_10_03-AM-08_25_44
Last ObjectModification:
2017_04_04-PM-06_40_00
Theory : reals
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