Nuprl - Proof: append split2

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At: append split2

T:Type, L:T List, P:(

||L||

Prop).

(

x:

||L||. Dec(P(x)))

(

i,j:

||L||. P(i)

i<j

P(j))

(

L_1,L_2:T List. L = (L_1 @ L_2) & (

i:

||L||. P(i)

||L_1||

i))

By:	Auto THEN Decide (i:\|\|L\|\|. P(i) & (j:i. P(j)))

Generated subgoals:

1 1. T : Type
2. L : T List
3. P : ||L||Prop
4. x:||L||. Dec(P(x))
5. i,j:||L||. P(i)  i<j  P(j)
6. i:||L||. P(i) & (j:i. P(j))
  L_1,L_2:T List. L = (L_1 @ L_2) & (i:||L||. P(i)  ||L_1||i)
8 steps

2 1. T : Type
2. L : T List
3. P : ||L||Prop
4. x:||L||. Dec(P(x))
5. i,j:||L||. P(i)  i<j  P(j)
6. (i:||L||. P(i) & (j:i. P(j)))
  L_1,L_2:T List. L = (L_1 @ L_2) & (i:||L||. P(i)  ||L_1||i)
11 steps

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