Nuprl Lemma : rmax-assoc

`∀[x,y,z:ℝ].  (rmax(rmax(x;y);z) = rmax(x;rmax(y;z)))`

Proof

Definitions occuring in Statement :  rmax: `rmax(x;y)` req: `x = y` real: `ℝ` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` real: `ℝ` squash: `↓T` rmax: `rmax(x;y)` prop: `ℙ` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q`
Lemmas referenced :  req_weakening rmax_wf equal_wf squash_wf true_wf imax_wf imax_assoc iff_weakening_equal nat_plus_wf regular-int-seq_wf req_witness real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_isectElimination because_Cache applyLambdaEquality setElimination rename sqequalRule imageMemberEquality baseClosed imageElimination dependent_set_memberEquality functionExtensionality applyEquality lambdaEquality equalityTransitivity equalitySymmetry universeEquality intEquality natural_numberEquality productElimination independent_functionElimination isect_memberEquality

Latex:
\mforall{}[x,y,z:\mBbbR{}].    (rmax(rmax(x;y);z)  =  rmax(x;rmax(y;z)))

Date html generated: 2017_10_03-AM-08_22_15
Last ObjectModification: 2017_07_28-AM-07_22_14

Theory : reals

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