Nuprl Lemma : rmin-idempotent
∀[x:ℝ]. (rmin(x;x) = x)
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uimplies: b supposing a
Lemmas referenced :
rmin-rleq,
rmin_ub,
rleq_weakening_equal,
rleq_antisymmetry,
req_witness,
rmin_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
productElimination,
hypothesis,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination
Latex:
\mforall{}[x:\mBbbR{}]. (rmin(x;x) = x)
Date html generated:
2016_05_18-AM-07_20_03
Last ObjectModification:
2015_12_28-AM-00_47_03
Theory : reals
Home
Index