Nuprl Lemma : rabs-of-nonneg

`∀[x:ℝ]. |x| = x supposing r0 ≤ x`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` rabs: `|x|` req: `x = y` int-to-real: `r(n)` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` top: `Top` implies: `P `` Q` prop: `ℙ` uiff: `uiff(P;Q)` and: `P ∧ Q` rev_uimplies: `rev_uimplies(P;Q)` all: `∀x:A. B[x]` itermConstant: `"const"` req_int_terms: `t1 ≡ t2` false: `False` not: `¬A` guard: `{T}`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin isect_memberEquality voidElimination voidEquality hypothesis hypothesisEquality independent_isectElimination independent_functionElimination natural_numberEquality because_Cache equalityTransitivity equalitySymmetry productElimination dependent_functionElimination computeAll lambdaEquality int_eqEquality intEquality addEquality lemma_by_obid

Latex:
\mforall{}[x:\mBbbR{}].  |x|  =  x  supposing  r0  \mleq{}  x

Date html generated: 2017_10_03-AM-08_30_46
Last ObjectModification: 2017_07_28-AM-07_26_44

Theory : reals

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