Nuprl Lemma : req_transitivity
∀[a,b,c:ℝ]. (a = c) supposing ((b = c) and (a = b))
Proof
Definitions occuring in Statement :
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Lemmas referenced :
req-equiv,
req_witness,
req_wf,
real_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
productElimination,
thin,
isect_memberFormation,
introduction,
isectElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}[a,b,c:\mBbbR{}]. (a = c) supposing ((b = c) and (a = b))
Date html generated:
2016_05_18-AM-06_50_33
Last ObjectModification:
2015_12_28-AM-00_29_02
Theory : reals
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