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| tactic | ::= | we need to prove term |
| | | we proceed by induction on term to prove term | |
| | | assume id : sterm | |
| | | by term done | |
| | | by induction hypothesis we know term ( id ) | |
| | | by term we proved term ( id ) | |
| | | case id ( id : term ) | |
| | | by term let id : term such that term ( id ) | |
| | | [obtain id | conclude term] = term by [ term | _ [(auto_params)]] [done] | |
| | | suppose term ( id ) [ that is equivalent to term ] | |
| | | the thesis becomes sterm | |
| | | we proceed by cases on term to prove term |