f74ae5f9c0
The notation `a ∈ as` for Arrays was previously only defined with `DecidableEq` on the elements, for (apparently) no good reason. This drops this requirements (by using `a ∈ as.data`), and simplifies a bunch of proofs by simply lifting the corresponding proof from lists. Also, `sizeOf_lt_of_mem` was defined, but not set up to be picked up by `decreasing_trivial` in the same way that the corresponding List lemma was set up, so this adds the tactic setup. The definition for `a ∈ as` is intentionally not defeq to `a ∈ as.data` so that the termination tactics for Arrays don’t spuriously apply when recursing through lists.
12 lines
596 B
Text
12 lines
596 B
Text
theorem Array.sizeOf_lt_of_mem' [DecidableEq α] [SizeOf α] {as : Array α} (h : as.contains a) : sizeOf a < sizeOf as := by
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simp [Membership.mem, contains, any, Id.run, BEq.beq, anyM] at h
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let rec aux (j : Nat) : anyM.loop (m := Id) (fun b => decide (a = b)) as as.size (Nat.le_refl ..) j = true → sizeOf a < sizeOf as := by
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unfold anyM.loop
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intro h
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split at h
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· simp [Bind.bind, pure] at h; split at h
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next he => subst a; apply sizeOf_get_lt
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next => have ih := aux (j+1) h; assumption
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· contradiction
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apply aux 0 h
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termination_by aux j => as.size - j
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