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Step * of Lemma face-term-distrib3

No Annotations
∀[Gamma:j⊢]. ∀[a,b,c:{Gamma ⊢ _:𝔽}].  Gamma ⊢ (((b ∨ c) ∧ a) ⇐⇒ ((b ∧ a) ∨ (c ∧ a)))
BY
{ (Auto
   THEN RepeatFor 2 (D 0)
   THEN Auto
   THEN (RepUR ``face-and face-or cubical-term-at`` -1 THEN Fold `cubical-term-at` (-1))
   THEN RepUR ``face-and face-or cubical-term-at`` 0
   THEN Fold `cubical-term-at` 0
   THEN (RWW "lattice-meet-eq-1 face_lattice-1-join-irreducible" (-1) THENA Auto)
   THEN (RWW "lattice-meet-eq-1 face_lattice-1-join-irreducible" 0 THENA Auto)
   THEN ProveProp
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[a,b,c:\{Gamma  \mvdash{}  \_:\mBbbF{}\}].    Gamma  \mvdash{}  (((b  \mvee{}  c)  \mwedge{}  a)  \mLeftarrow{}{}\mRightarrow{}  ((b  \mwedge{}  a)  \mvee{}  (c  \mwedge{}  a)))


By

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Latex:
(Auto
  THEN  RepeatFor  2  (D  0)
  THEN  Auto
  THEN  (RepUR  ``face-and  face-or  cubical-term-at``  -1  THEN  Fold  `cubical-term-at`  (-1))
  THEN  RepUR  ``face-and  face-or  cubical-term-at``  0
  THEN  Fold  `cubical-term-at`  0
  THEN  (RWW  "lattice-meet-eq-1  face\_lattice-1-join-irreducible"  (-1)  THENA  Auto)
  THEN  (RWW  "lattice-meet-eq-1  face\_lattice-1-join-irreducible"  0  THENA  Auto)
  THEN  ProveProp
  THEN  Auto)

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