`∀[a,b,c:ℝ].  (((a + b) + c) = (a + b + c))`

Proof

Definitions occuring in Statement :  req: `x = y` radd: `a + b` real: `ℝ` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` subtype_rel: `A ⊆r B` uimplies: `b supposing a` true: `True` squash: `↓T` prop: `ℙ` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)` append: `as @ bs` all: `∀x:A. B[x]` so_lambda: `so_lambda(x,y,z.t[x; y; z])` top: `Top` so_apply: `x[s1;s2;s3]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality independent_functionElimination sqequalRule isect_memberEquality because_Cache applyEquality independent_isectElimination natural_numberEquality lambdaEquality imageElimination equalityTransitivity equalitySymmetry universeEquality imageMemberEquality baseClosed productElimination hyp_replacement applyLambdaEquality dependent_functionElimination voidElimination voidEquality

Latex:
\mforall{}[a,b,c:\mBbbR{}].    (((a  +  b)  +  c)  =  (a  +  b  +  c))

Date html generated: 2017_10_02-PM-07_15_32
Last ObjectModification: 2017_07_28-AM-07_20_32

Theory : reals

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