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feat: add Löb induction example #151

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markusdemedeiros merged 1 commit into from
Feb 5, 2026
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feat: add Löb induction example #151

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19 changes: 18 additions & 1 deletion src/Iris/Examples/IProp.lean
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Expand Up @@ -172,7 +172,7 @@ example (e e' : Expr) Φ (Hstep : ∀ {s : State}, @step _ _ Value _ (e, s) = (e
Then, it suffies to have access to P, and show that access to P' is enough to verify e'. -/
example (e e' : Expr) (P P' : IProp GF) Φ
(Hstep : ∀ s, iprop(P ∗ @state_interp State GF _ s ⊢ ∃ s',
⌜@step _ _ Value _ (e, s) = (e', s')⌝ ∗ |==> (P' ∗ @state_interp State GF _ s'))) :
⌜ step Value (e, s) = (e', s')⌝ ∗ |==> (P' ∗ @state_interp State GF _ s'))) :
P ∗ (P' -∗ wp e' Φ) ⊢ wp e Φ := by
iintro ⟨HP, Hspec⟩
iapply wp_unfold
Expand All @@ -190,6 +190,23 @@ example (e e' : Expr) (P P' : IProp GF) Φ
· iexact Hs
· iapply Hspec $$ HP'

/- Looping programs, by Löb induction -/
example (e : Expr) Φ (Hloop : ∀ σ : State, step Value (e, σ) = (e, σ)) :
⊢ wp e Φ := by
iapply BILoeb.loeb_weak
iintro HLöb
iapply wp_unfold
iright
iintro %s Hs
iexists e, s
isplitr
· ipure_intro; exact Hloop s
iintro !> !>
isplitl [Hs]
· iassumption
· iassumption
· exact true_intro

end Example3

end Iris.Examples
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