cdlemg6a

Description: TODO: FIX COMMENT. TODO: replace with cdlemg4 . (Contributed by NM, 27-Apr-2013)

	Ref	Expression
Hypotheses	cdlemg4.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
	cdlemg4.a	$⊢ A = Atoms (K)$
	cdlemg4.h	$⊢ H = LHyp (K)$
	cdlemg4.t	$⊢ T = LTrn (K) (W)$
	cdlemg4.r	$⊢ R = trL (K) (W)$
	cdlemg4.j	$⊢ \underset{˙}{\lor} = join (K)$
	cdlemg4b.v	$⊢ V = R (G)$
Assertion	cdlemg6a	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (r \in A \land \neg r \underset{˙}{\leq} W) \land F \in T) \land (G \in T \land \neg r \underset{˙}{\leq} (P \underset{˙}{\lor} V) \land F (G (P)) = P)) \to F (G (r)) = r$

Step	Hyp	Ref	Expression
1		cdlemg4.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
2		cdlemg4.a	$⊢ A = Atoms (K)$
3		cdlemg4.h	$⊢ H = LHyp (K)$
4		cdlemg4.t	$⊢ T = LTrn (K) (W)$
5		cdlemg4.r	$⊢ R = trL (K) (W)$
6		cdlemg4.j	$⊢ \underset{˙}{\lor} = join (K)$
7		cdlemg4b.v	$⊢ V = R (G)$
8	1 2 3 4 5 6 7	cdlemg4	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (r \in A \land \neg r \underset{˙}{\leq} W) \land F \in T) \land (G \in T \land \neg r \underset{˙}{\leq} (P \underset{˙}{\lor} V) \land F (G (P)) = P)) \to F (G (r)) = r$

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