Nuprl Lemma : req*-equiv
EquivRel(ℝ*;x,y.x = y)
Proof
Definitions occuring in Statement :
req*: x = y,
real*: ℝ*,
equiv_rel: EquivRel(T;x,y.E[x; y])
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
member: t ∈ T,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
guard: {T},
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
uimplies: b supposing a
Lemmas referenced :
real*_wf,
req*_inversion,
req*_wf,
req*_transitivity,
req*_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
independent_isectElimination
Latex:
EquivRel(\mBbbR{}*;x,y.x = y)
Date html generated:
2018_05_22-PM-03_14_45
Last ObjectModification:
2017_10_06-PM-02_12_25
Theory : reals_2
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