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Step * 1 1 of Lemma real-ring_wf


1. λx,y. (x + y) ∈ (x,y:ℝ//(x = y)) ⟶ (x,y:ℝ//(x = y)) ⟶ (x,y:ℝ//(x = y))
2. λx,y. (x * y) ∈ (x,y:ℝ//(x = y)) ⟶ (x,y:ℝ//(x = y)) ⟶ (x,y:ℝ//(x = y))
3. λx.-(x) ∈ (x,y:ℝ//(x = y)) ⟶ (x,y:ℝ//(x = y))
⊢ real-ring() ∈ RngSig
BY
{ (RepUR ``real-ring rng_sig`` 0 THEN Auto) }

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Latex:

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Latex:

1.  \mlambda{}x,y.  (x  +  y)  \mmember{}  (x,y:\mBbbR{}//(x  =  y))  {}\mrightarrow{}  (x,y:\mBbbR{}//(x  =  y))  {}\mrightarrow{}  (x,y:\mBbbR{}//(x  =  y))
2.  \mlambda{}x,y.  (x  *  y)  \mmember{}  (x,y:\mBbbR{}//(x  =  y))  {}\mrightarrow{}  (x,y:\mBbbR{}//(x  =  y))  {}\mrightarrow{}  (x,y:\mBbbR{}//(x  =  y))
3.  \mlambda{}x.-(x)  \mmember{}  (x,y:\mBbbR{}//(x  =  y))  {}\mrightarrow{}  (x,y:\mBbbR{}//(x  =  y))
\mvdash{}  real-ring()  \mmember{}  RngSig


By

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Latex:
(RepUR  ``real-ring  rng\_sig``  0  THEN  Auto)

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