Examples from MoSeL paper.

tests/mosel_paper.ref

+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  ============================
+  "HP" : P
+  "H" : ∃ a : A, Φ a ∨ Ψ a
+  --------------------------------------∗
+  ∃ a : A, P ∗ Φ a ∨ P ∗ Ψ a
+  
+2 subgoals
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  x : A
+  ============================
+  "HP" : P
+  "H1" : Φ x
+  --------------------------------------∗
+  ∃ a : A, P ∗ Φ a ∨ P ∗ Ψ a
+  
+
+subgoal 2 is:
+ "HP" : P
+"H2" : Ψ x
+--------------------------------------∗
+∃ a : A, P ∗ Φ a ∨ P ∗ Ψ a
+
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  ============================
+  "HP" : P
+  "H" : ∃ a : A, Φ a ∨ Ψ a
+  --------------------------------------∗
+  ∃ a : A, P ∗ Φ a ∨ P ∗ Ψ a
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  ============================
+  "H" : ∃ a : A, Φ a ∨ Ψ a
+  --------------------------------------∗
+  ∃ x : A, Φ x ∨ Ψ x
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  x : A
+  ============================
+  "HP" : <affine> P
+  "H1" : Φ x
+  --------------------------------------∗
+  Φ x
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  x : A
+  ============================
+  "HP" : <affine> P
+  "H2" : Ψ x
+  --------------------------------------∗
+  P ∗ Ψ x
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  ============================
+  "HP" : P
+  --------------------------------------□
+  "H" : ∃ a : A, Φ a ∨ Ψ a
+  --------------------------------------∗
+  ∃ a : A, Φ a ∨ P ∗ P ∗ Ψ a
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P : PROP
+  Φ, Ψ : A → PROP
+  x : A
+  ============================
+  "HP" : P
+  --------------------------------------□
+  "H2" : Ψ x
+  --------------------------------------∗
+  P ∗ P ∗ Ψ x
+  
+1 subgoal
+  
+  PROP : bi
+  A : Type
+  P, Q : PROP
+  ============================
+  "HP" : P
+  "HQ" : Q
+  --------------------------------------□
+  □ (P ∗ Q)
+  
+1 subgoal
+  
+  I : biIndex
+  PROP : bi
+  Φ, Ψ : monPred I PROP
+  ============================
+  "H1" : Φ
+  "H2" : Φ -∗ Ψ
+  --------------------------------------∗
+  Ψ
+  
+1 subgoal
+  
+  I : biIndex
+  PROP : bi
+  Φ, Ψ : monPred I PROP
+  ============================
+  --------------------------------------∗
+  ∀ i : I, Φ i ∗ (Φ -∗ Ψ) i -∗ Ψ i
+  
+1 subgoal
+  
+  I : biIndex
+  PROP : bi
+  Φ : monPred I PROP
+  P, Q : PROP
+  ============================
+  "H2" : ⎡ P ⎤
+  --------------------------------------□
+  "H1" : ⎡ P -∗ Q ⎤
+  "H3" : <affine> Φ
+  --------------------------------------∗
+  ⎡ P ∗ Q ⎤
+  
+1 subgoal
+  
+  I : biIndex
+  PROP : bi
+  Φ : monPred I PROP
+  P, Q : PROP
+  ============================
+  "H2" : ⎡ P ⎤
+  --------------------------------------□
+  "H1" : ⎡ P -∗ Q ⎤
+  "H3" : <affine> Φ
+  --------------------------------------∗
+  ⎡ Q ⎤
+  

tests/mosel_paper.v

+(** This file contains the examples from the paper:
+
+MoSeL: A General, Extensible Modal Framework for Interactive Proofs in
+Separation Logic
+Robbert Krebbers, Jacques-Henri Jourdan, Ralf Jung, Joseph Tassarotti,
+Jan-Oliver Kaiser, Amin Timany, Arthur Charguéraud, Derek Dreyer
+ICFP 2018 *)
+From iris.proofmode Require Import tactics monpred.
+From iris.bi Require Import monpred.
+
+Lemma example_1 {PROP : bi} {A : Type} (P : PROP) (Φ Ψ : A → PROP) :
+  P ∗ (∃ a, Φ a ∨ Ψ a) -∗ ∃ a, (P ∗ Φ a) ∨ (P ∗ Ψ a).
+Proof.
+  iIntros "[HP H]". Show.
+  iDestruct "H" as (x) "[H1|H2]". Show.
+  - iExists x. iLeft. iSplitL "HP"; iAssumption.
+  - iExists x. iRight. iSplitL "HP"; iAssumption.
+Qed.
+Lemma example {PROP : bi} {A : Type} (P : PROP) (Φ Ψ : A → PROP) :
+P ∗ (∃ a, Φ a ∨ Ψ a) -∗ ∃ a, (P ∗ Φ a) ∨ (P ∗ Ψ a).
+Proof.
+  iIntros "[HP H]". Show.
+  iFrame "HP". Show.
+  iAssumption.
+Qed.
+
+Lemma example_2 {PROP : bi} {A : Type} (P : PROP) (Φ Ψ : A → PROP) :
+  <affine> P ∗ (∃ a, Φ a ∨ Ψ a) -∗ ∃ a, Φ a ∨ (P ∗ Ψ a).
+Proof.
+  iIntros "[HP H]". iDestruct "H" as (x) "[H1|H2]".
+  - iExists x. iLeft. Show. iAssumption.
+  - iExists x. iRight. Show. iSplitL "HP"; iAssumption.
+Qed.
+
+Lemma example_3 {PROP : bi} {A : Type} (P : PROP) (Φ Ψ : A → PROP) :
+  □ P ∗ (∃ a, Φ a ∨ Ψ a) -∗ ∃ a, Φ a ∨ (P ∗ P ∗ Ψ a).
+Proof.
+  iIntros "[#HP H]". Show. iDestruct "H" as (x) "[H1|H2]".
+  - iExists x. iLeft. iAssumption.
+  - iExists x. iRight. Show. iSplitR; [|iSplitR]; iAssumption.
+Qed.
+Lemma example_4 {PROP : bi} {A : Type} (P Q : PROP) : □ P ∧ □ Q -∗ □ (P ∗ Q).
+Proof. iIntros "[#HP #HQ]". Show. iModIntro. iSplitL; iAssumption. Qed.
+
+Lemma example_monpred {I PROP} (Φ Ψ : monPred I PROP) : Φ ∗ (Φ -∗ Ψ) ⊢ Ψ.
+Proof. iIntros "[H1 H2]". Show. iApply "H2". iAssumption. Qed.
+
+Lemma example_monpred_model {I PROP} (Φ Ψ : monPred I PROP) : Φ ∗ (Φ -∗ Ψ) ⊢ Ψ.
+Proof. iStartProof PROP. Show. iIntros (i) "[H1 H2]". iApply "H2". iAssumption. Qed.
+
+Lemma example_monpred_2 {I PROP} (Φ : monPred I PROP) (P Q : PROP) :
+  ⎡ P -∗ Q ⎤ -∗ ⎡ □ P ⎤ -∗ <affine> Φ -∗ ⎡ P ∗ Q ⎤.
+Proof. iIntros "H1 #H2 H3". Show. iFrame "H2". Show. iApply "H1". iAssumption. Qed.