如何用Isabelle/HOL证明下列陈述？

Question

有人能帮我用伊莎贝尔/霍尔中的下列方程(一阶逻辑)证明X=M吗？

N>=M

forall n. 0=<n<N --> n<M

X=N

其中N, M, X是整数常量。n整数变量.

Answer 1

只有当变量是自然变量，而不是整数时，才能进行证明，例如使用此证明：

theory Scratch
imports Main
begin
theorem
  fixes N M X :: nat
  assumes "N ≥ M"
  assumes "∀ n. (0 ≤ n ∧ n < N) ⟶ n<M"
  assumes "X = N"
  shows "X = M"
proof-
  have "¬ N > M"
  proof
    assume "M < N" with `∀ n. _` show False by auto
  qed
  with `N ≥ M` and `X = N`
  show "X = M" by auto
qed

end

如果允许整数而不是反例，则为M=-2、N=-1和X=-2.