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Proof step 129 from proof rg2-lem1-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N = N'' + 1 until Boolvar, [:S | Boolvar ::- [PL N = n23 ∧ S = s31 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s32 ∧ N = n24 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(N + 1) ∧ INDHYP-nat0(N + 1), n23 = N, R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), I(pm, s), G1(pm, s2, s2), R1(pm, s2, s31), G2(pm, s2, s3), R2(pm, s3, s32), n24 ≤ N + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s31), I(pm, S), I(pm, s32), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ ◇ last, [:S | Boolvar ::- [PL N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ]

User applied rule decompose

And closed the goal!

Rule argument

positions: 3, 2

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