cdlemg10b

Description: TODO: FIX COMMENT. TODO: Can this be moved up as a stand-alone theorem in ltrn* area? (Contributed by NM, 4-May-2013)

	Ref	Expression
Hypotheses	cdlemg8.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
	cdlemg8.j	$⊢ \underset{˙}{\lor} = join (K)$
	cdlemg8.m	$⊢ \underset{˙}{\land} = meet (K)$
	cdlemg8.a	$⊢ A = Atoms (K)$
	cdlemg8.h	$⊢ H = LHyp (K)$
	cdlemg8.t	$⊢ T = LTrn (K) (W)$
Assertion	cdlemg10b	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (Q \in A \land \neg Q \underset{˙}{\leq} W)) \land F \in T) \to (F (P) \underset{˙}{\lor} F (Q)) \underset{˙}{\land} W = (P \underset{˙}{\lor} Q) \underset{˙}{\land} W$

Step	Hyp	Ref	Expression
1		cdlemg8.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
2		cdlemg8.j	$⊢ \underset{˙}{\lor} = join (K)$
3		cdlemg8.m	$⊢ \underset{˙}{\land} = meet (K)$
4		cdlemg8.a	$⊢ A = Atoms (K)$
5		cdlemg8.h	$⊢ H = LHyp (K)$
6		cdlemg8.t	$⊢ T = LTrn (K) (W)$
7		eqid	$⊢ (P \underset{˙}{\lor} Q) \underset{˙}{\land} W = (P \underset{˙}{\lor} Q) \underset{˙}{\land} W$
8	5 6 1 2 4 3 7	cdlemg2m	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (Q \in A \land \neg Q \underset{˙}{\leq} W)) \land F \in T) \to (F (P) \underset{˙}{\lor} F (Q)) \underset{˙}{\land} W = (P \underset{˙}{\lor} Q) \underset{˙}{\land} W$

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