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Proof step 6 from proof fair-sustains-implies-always (previous step)

[:S | [PL □ 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'))]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, S), I(pm, s) ⊦ [:S | [PL □ (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')))]]

User applied rule cut formula

And obtained the following new goals

Proof step 7:
[:S | [PL □ R1(pm, S', S'') ∧ □ (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL □ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∨ ◇ ¬ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ] ], [:S | [PL □ 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'))]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, S), I(pm, s) ⊦ [:S | [PL □ (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')))]]
Proof step 68:
[:S | [PL □ 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'))]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, S), I(pm, s) ⊦ [:S | [PL □ R1(pm, S', S'') ∧ □ (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL □ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∨ ◇ ¬ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ] ], [:S | [PL □ (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')))]]

Rule argument

fma: [:S | [PL □ R1(pm, S', S'') ∧ □ (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ] ∥ [PL □ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∨ ◇ ¬ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ] ]

Additional information

Used formulas: [:S | [PL □ R1(pm, S', S'') ∧ □ (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL □ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∨ ◇ ¬ R2(pm, S', S'') ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ] ]