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Theorem base for Specification Progress-I-2-Theory

This is a listing of all goals defined over the current specification. Axioms are yellow, proof obligations purple and theorems green. Click on individual names to get more information on the proof.

Name: Sequent: Type:
P-restr-def ⊦ P-restr(pm, P, I, R) ↔ (∀ s, s0. I(pm, s) ∧ I(pm, s0) ∧ P(pm, s) ∧ R(pm, s, s0) → P(pm, s0)) An Axiom
notP-def ⊦ (¬ P)(pm, s) ↔ ¬ P(pm, s) An Axiom
stable-def ⊦ stable(pm, I, R) ↔ (∀ s, s0. I(pm, s) ∧ R(pm, s, s0) → I(pm, s0)) An Axiom
no-init-violation-leftRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL ¬ P(pm, S)] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]], P(pm, S) ⊦ A User Theorem
no-init-violation-rightRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R2), Pre1(pm, s), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL ¬ P(pm, S)]], P(pm, S) ⊦ A User Theorem
no-progress-fw ⊦ P-restr(pm, ¬ P, I, R) ∧ ¬ P(pm, s) ∧ R(pm, s, s0) ∧ I(pm, s) ∧ I(pm, s0) → ¬ P(pm, s0) A User Theorem
no-progress-leftRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL ◇ □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ ◇ □ (¬ P(pm, S) ∧ ¬ last) A User Theorem
no-progress-left-auxRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ □ (¬ P(pm, S) ∧ ¬ last) A User Theorem
no-progress-left-aux0RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ], P(pm, S) ∨ last ⊦ A User Theorem
no-progress-rightRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R2), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL ◇ □ (¬ P(pm, S) ∧ ¬ last) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ ◇ □ (¬ P(pm, S) ∧ ¬ last) A User Theorem
no-progress-right-auxRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R2), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ □ (¬ P(pm, S) ∧ ¬ last) A User Theorem
progress-fw ⊦ P-restr(pm, P, I, R) ∧ P(pm, s) ∧ R(pm, s, s0) ∧ I(pm, s) ∧ I(pm, s0) → P(pm, s0) A User Theorem
progress-leftRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ □ ◇ P(pm, S) A User Theorem
progress-left-auxRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ ◇ P(pm, S) A User Theorem
progress-rightRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R2), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL □ ◇ P(pm, S) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ □ ◇ P(pm, S) A User Theorem
progress-right-auxRG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R2), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL ◇ P(pm, S) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ⊦ ◇ P(pm, S) A User Theorem
stable-fw ⊦ stable(pm, I, R) ∧ I(pm, s) ∧ R(pm, s, s0) → I(pm, s0) A User Theorem