Quick reference card
assume
suppose
by done
we need to prove
we proceed by induction
we proceed by cases
by induction
thesis becomes
case
obtain/conclude
by term we proved
exits elim
and elim

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