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Step * of Lemma sq_or_functionality_wrt_iff

∀[P1,P2,Q1,Q2:ℙ].  ({P1 ⇐⇒ P2} ⇒ {Q1 ⇐⇒ Q2} ⇒ {P1 ↓∨ Q1 ⇐⇒ P2 ↓∨ Q2})
BY
{ (Unfold `guard` 0
   THEN Unfold `sq_or` 0
   THEN Auto
   THEN D -1
   THEN ThinTrivial
   THEN D 0
   THEN ((OrLeft THENM Trivial) ORELSE (OrRight THENM Trivial))
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}].    (\{P1  \mLeftarrow{}{}\mRightarrow{}  P2\}  {}\mRightarrow{}  \{Q1  \mLeftarrow{}{}\mRightarrow{}  Q2\}  {}\mRightarrow{}  \{P1  \mdownarrow{}\mvee{}  Q1  \mLeftarrow{}{}\mRightarrow{}  P2  \mdownarrow{}\mvee{}  Q2\})


By

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Latex:
(Unfold  `guard`  0
  THEN  Unfold  `sq\_or`  0
  THEN  Auto
  THEN  D  -1
  THEN  ThinTrivial
  THEN  D  0
  THEN  ((OrLeft  THENM  Trivial)  ORELSE  (OrRight  THENM  Trivial))
  THEN  Auto)

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