cdleme43frv1snN

Description: Value of [_ R / s ]_ N when -. R .<_ ( P .\/ Q ) . (Contributed by NM, 30-Mar-2013) (New usage is discouraged.)

	Ref	Expression
Hypotheses	cdlemefr27.b	$⊢ B = {Base}_{K}$
	cdlemefr27.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
	cdlemefr27.j	$⊢ \underset{˙}{\lor} = join (K)$
	cdlemefr27.m	$⊢ \underset{˙}{\land} = meet (K)$
	cdlemefr27.a	$⊢ A = Atoms (K)$
	cdlemefr27.h	$⊢ H = LHyp (K)$
	cdlemefr27.u	$⊢ U = (P \underset{˙}{\lor} Q) \underset{˙}{\land} W$
	cdlemefr27.c	$⊢ C = (s \underset{˙}{\lor} U) \underset{˙}{\land} (Q \underset{˙}{\lor} ((P \underset{˙}{\lor} s) \underset{˙}{\land} W))$
	cdlemefr27.n	$⊢ N = if (s \underset{˙}{\leq} (P \underset{˙}{\lor} Q), I, C)$
	cdleme43fr.x	$⊢ X = (R \underset{˙}{\lor} U) \underset{˙}{\land} (Q \underset{˙}{\lor} ((P \underset{˙}{\lor} R) \underset{˙}{\land} W))$
Assertion	cdleme43frv1snN	$⊢ (R \in A \land \neg R \underset{˙}{\leq} (P \underset{˙}{\lor} Q)) \to ⦋ R / s ⦌ N = X$

Step	Hyp	Ref	Expression
1		cdlemefr27.b	$⊢ B = {Base}_{K}$
2		cdlemefr27.l	$⊢ \underset{˙}{\leq} = \leq_{K}$
3		cdlemefr27.j	$⊢ \underset{˙}{\lor} = join (K)$
4		cdlemefr27.m	$⊢ \underset{˙}{\land} = meet (K)$
5		cdlemefr27.a	$⊢ A = Atoms (K)$
6		cdlemefr27.h	$⊢ H = LHyp (K)$
7		cdlemefr27.u	$⊢ U = (P \underset{˙}{\lor} Q) \underset{˙}{\land} W$
8		cdlemefr27.c	$⊢ C = (s \underset{˙}{\lor} U) \underset{˙}{\land} (Q \underset{˙}{\lor} ((P \underset{˙}{\lor} s) \underset{˙}{\land} W))$
9		cdlemefr27.n	$⊢ N = if (s \underset{˙}{\leq} (P \underset{˙}{\lor} Q), I, C)$
10		cdleme43fr.x	$⊢ X = (R \underset{˙}{\lor} U) \underset{˙}{\land} (Q \underset{˙}{\lor} ((P \underset{˙}{\lor} R) \underset{˙}{\land} W))$
11	8 9 10	cdleme31sn2	$⊢ (R \in A \land \neg R \underset{˙}{\leq} (P \underset{˙}{\lor} Q)) \to ⦋ R / s ⦌ N = X$

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