8b0dd2e835
This will collect definitions from Std.Logic --------- Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
12 lines
610 B
Text
12 lines
610 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 only [bind, decide_eq_true_eq, 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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termination_by as.size - j
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apply aux 0 h
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