我有这个目标,我想证明这一点。
1 goal
t1, t2 : FCPLang
H : evalS t1 = Some t2
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evalBS t1 = evalBS t2
为了证明这一点,我使用了induction t1.
,但这些是引入的归纳假设:
1 goal
t1_1, t1_2, t1_3, t2 : FCPLang
H : evalS (if_then_else t1_1 t1_2 t1_3) = Some t2
IHt1_1 : evalS t1_1 = Some t2 -> evalBS t1_1 = evalBS t2
IHt1_2 : evalS t1_2 = Some t2 -> evalBS t1_2 = evalBS t2
IHt1_3 : evalS t1_3 = Some t2 -> evalBS t1_3 = evalBS t2
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evalBS (if_then_else t1_1 t1_2 t1_3) = evalBS t2
我认为这毫无用处,因为t2
再次使用它们,而不是引入一个新术语,例如:
IHt1_1 : evalS t1_1 = Some t2_1 -> evalBS t1_1 = evalBS t2_1
我该如何解决这个问题?