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@@ -604,6 +604,12 @@ by
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| snd h ih => exact analz.snd ih
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| decrypt h₁ h₂ ih₁ ih₂ => exact analz.decrypt ih₁ ih₂
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@[grind .]
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lemma analz_insert_mono [InvKey] :
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X ∈ analz H → X ∈ analz (insert Y H)
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:= by
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apply_rules [ analz_mono, Set.subset_insert]
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lemma analz_mono_neg [InvKey] { h : A ⊆ B } :
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X ∉ analz B → X ∉ analz A
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:= by
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@@ -624,7 +630,7 @@ by
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· apply analz.fst h
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· apply analz.snd h
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@[simp]
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@[simp, grind! .]
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lemma analz_increasing [InvKey] {H : Set Msg} : H ⊆ analz H :=
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λ _ hx => analz.inj hx
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@@ -637,6 +643,7 @@ by
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| snd _ ih => aapply parts.snd
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| decrypt _ _ ih₁ => aapply parts.body
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@[grind! .]
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lemma analz_subset_parts {H : Set Msg} [InvKey] : analz H ⊆ parts H :=
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λ _ hx => analz_into_parts hx
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@@ -1628,5 +1635,3 @@ X ∈ A ∨ h₁ → X ∈ B ∨ h₁
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intro h; cases h <;> try simp_all
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left; aapply h
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attribute [-simp] Key.injEq
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