Nuprl - Proof: card split sigma dom decbl 1

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At: card split sigma dom decbl 1

1. A : Type
2. B : A

Type
3. P : A

Prop
4.

i:A. Dec(P(i))

(i:A

B(i)) ~ ((i:{i:A| P(i) }

B(i))+(i:{i:A|

P(i) }

B(i)))

By:	Inst: Thm* (x:A. Dec(P(x))) (A ~ ({x:A\| P(x) }+{x:A\| P(x) })) Using:[A:= i:AB(i) \| P(x):= P(x/x,y. x)] ; Rewrite by Thm* B:(AType), P:(AProp). Thm* (i:{i:A\| P(i) }B(i)) ~ {v:(i:AB(i))\| P(v/x,y. x) }

Generated subgoal:

1 (i:AB(i)) ~ ({v:(i:AB(i))| P(v/x,y. x) }+{v:(i:AB(i))| P(v/x,y. x) })
2 steps

About:

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