Level: Lib Thy Top: 2 1
Hypotheses:

  1. n : {1 + 1...}

  2. f:((n - 1) + 1) (n - 1). i:((n - 1) + 1). j:i. f i = f j

  3. f : (n + 1) n

Conclusion:

iii:(n + 1) (ii:{(iii + 1)..(n + 1)}. jj:ii. (f ii = f jj)) (i:(iii + 1). j:i. f i = f j)


Applied Tactic: (BLemma `int_seg_ind` THENM All ArithSimp ...a)
Generated subgoals:

1. (ii:{1..(1 + n)}. jj:ii. (f ii = f jj)) (i:1. j:i. f i = f j)

2. iii:{1..(1 + n)} ((ii:{iii..(1 + n)}. jj:ii. (f ii = f jj)) (i:iii. j:i. f i = f j)) (ii:{(1 + iii)..(1 + n)}. jj:ii. (f ii = f jj)) (i:(1 + iii). j:i. f i = f j)