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Proof step 7 from proof progress-left-aux (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, G1(pm, s2, s3) ∧ ¬ boolvar ∧ ¬ R1(pm, s3, s0) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL S = s0 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∨ G1(pm, s2, s2) ∧ G2(pm, s2, s3) ∧ ¬ boolvar ∧ ¬ R1(pm, s2, s1) ∧ ¬ R2(pm, s3, s4) ∧ [:S | Boolvar ::- [PL S = s1 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s4]] ∨ G1(pm, s2, s2) ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s6) ∧ ¬ boolvar ∧ ¬ R1(pm, s2, s5) ∧ [:S | Boolvar ::- [PL S = s5 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s6 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∨ G1(pm, s2, s3) ∧ R1(pm, s3, s7) ∧ ¬ boolvar ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL S = s7 ∧ ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∨ G1(pm, s2, s2) ∧ R1(pm, s2, s8) ∧ G2(pm, s2, s3) ∧ ¬ boolvar ∧ ¬ R2(pm, s3, s9) ∧ [:S | Boolvar ::- [PL S = s8 ∧ ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s9]] ∨ G1(pm, s2, s2) ∧ R1(pm, s2, s10) ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s11) ∧ ¬ boolvar ∧ [:S | Boolvar ::- [PL S = s10 ∧ ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s11 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∨ ¬ boolvar ∧ G2(pm, s2, s3) ∧ ¬ R2(pm, s3, s12) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s12]] ∨ G2(pm, s2, s2) ∧ G1(pm, s2, s3) ∧ ¬ R2(pm, s2, s13) ∧ ¬ boolvar ∧ ¬ R1(pm, s3, s14) ∧ [:S | Boolvar ::- [PL S = s14 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s13]] ∨ G2(pm, s2, s2) ∧ G1(pm, s2, s3) ∧ R1(pm, s3, s16) ∧ ¬ R2(pm, s2, s15) ∧ ¬ boolvar ∧ [:S | Boolvar ::- [PL S = s16 ∧ ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s15]] ∨ ¬ boolvar ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s17) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s17 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∨ G2(pm, s2, s2) ∧ R2(pm, s2, s18) ∧ G1(pm, s2, s3) ∧ ¬ boolvar ∧ ¬ R1(pm, s3, s19) ∧ [:S | Boolvar ::- [PL S = s19 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s18 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∨ G2(pm, s2, s2) ∧ R2(pm, s2, s20) ∧ G1(pm, s2, s3) ∧ R1(pm, s3, s21) ∧ ¬ boolvar ∧ [:S | Boolvar ::- [PL S = s21 ∧ ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL S = s20 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ], \A ∀ N, R1, pm, S, R2, Boolvar, P, Post1, s, G1, Post2, G2, Pre1, I, Pre2. N < n → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∧ RG-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) ∧ P-restr(pm, P, I, R1) → ◇ P(pm, S), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, s2), Pre1(pm, s), Pre2(pm, s), P-restr(pm, P, I, R1), R1(pm, s3, S), R2(pm, s3, S), ¬ P(pm, s2), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n = n0 ⊦ ◇ P(pm, S)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 3

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