cdlemg25zz

Description: cdlemg16zz restated for easier studying. TODO: Discard this after everything is figured out. (Contributed by NM, 26-May-2013)

	Ref	Expression
Hypotheses	cdlemg12.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
	cdlemg12.j	$⊢ \underset{˙}{\lor} = join (K)$
	cdlemg12.m	$⊢ \underset{˙}{\land} = meet (K)$
	cdlemg12.a	$⊢ A = Atoms (K)$
	cdlemg12.h	$⊢ H = LHyp (K)$
	cdlemg12.t	$⊢ T = LTrn (K) (W)$
	cdlemg12b.r	$⊢ R = trL (K) (W)$
Assertion	cdlemg25zz	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (z \in A \land \neg z \underset{˙}{\leq} W) \land F \in T) \land (G \in T \land \neg R (F) \underset{˙}{\leq} (P \underset{˙}{\lor} z) \land \neg R (G) \underset{˙}{\leq} (P \underset{˙}{\lor} z))) \to (P \underset{˙}{\lor} F (G (P))) \underset{˙}{\land} W = (z \underset{˙}{\lor} F (G (z))) \underset{˙}{\land} W$

Step	Hyp	Ref	Expression
1		cdlemg12.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
2		cdlemg12.j	$⊢ \underset{˙}{\lor} = join (K)$
3		cdlemg12.m	$⊢ \underset{˙}{\land} = meet (K)$
4		cdlemg12.a	$⊢ A = Atoms (K)$
5		cdlemg12.h	$⊢ H = LHyp (K)$
6		cdlemg12.t	$⊢ T = LTrn (K) (W)$
7		cdlemg12b.r	$⊢ R = trL (K) (W)$
8	1 2 3 4 5 6 7	cdlemg16zz	$⊢ ((K \in HL \land W \in H) \land ((P \in A \land \neg P \underset{˙}{\leq} W) \land (z \in A \land \neg z \underset{˙}{\leq} W) \land F \in T) \land (G \in T \land \neg R (F) \underset{˙}{\leq} (P \underset{˙}{\lor} z) \land \neg R (G) \underset{˙}{\leq} (P \underset{˙}{\lor} z))) \to (P \underset{˙}{\lor} F (G (P))) \underset{˙}{\land} W = (z \underset{˙}{\lor} F (G (z))) \underset{˙}{\land} W$

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