### Nuprl Lemma : rleq_weakening_equal

`∀[x,y:ℝ].  x ≤ y supposing x = y ∈ ℝ`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` guard: `{T}` rleq: `x ≤ y` rnonneg: `rnonneg(x)` all: `∀x:A. B[x]` le: `A ≤ B` and: `P ∧ Q` not: `¬A` implies: `P `` Q` false: `False` subtype_rel: `A ⊆r B` real: `ℝ` prop: `ℙ`
Lemmas referenced :  rleq_weakening req_weakening less_than'_wf rsub_wf real_wf nat_plus_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination because_Cache sqequalRule lambdaEquality dependent_functionElimination productElimination independent_pairEquality applyEquality setElimination rename minusEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality voidElimination

Latex:
\mforall{}[x,y:\mBbbR{}].    x  \mleq{}  y  supposing  x  =  y

Date html generated: 2016_10_26-AM-09_06_37
Last ObjectModification: 2016_08_04-PM-03_58_59

Theory : reals

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