### Nuprl Lemma : rmul-rsub-distrib

`∀[a,b,c:ℝ].  (((a * (b - c)) = ((a * b) - a * c)) ∧ (((b - c) * a) = ((b * a) - c * a)))`

Proof

Definitions occuring in Statement :  rsub: `x - y` req: `x = y` rmul: `a * b` real: `ℝ` uall: `∀[x:A]. B[x]` and: `P ∧ Q`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` and: `P ∧ Q` cand: `A c∧ B` implies: `P `` Q` uimplies: `b supposing a` rsub: `x - y` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  req_witness rmul_wf rsub_wf real_wf radd_wf rminus_wf req_weakening req_wf req_functionality req_transitivity rmul-distrib radd_functionality rmul_over_rminus uiff_transitivity rminus_functionality rmul_comm
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation hypothesis sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality extract_by_obid isectElimination hypothesisEquality independent_functionElimination isect_memberEquality because_Cache independent_isectElimination

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

Date html generated: 2017_10_02-PM-07_17_35
Last ObjectModification: 2017_07_28-AM-07_21_12

Theory : reals

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