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Proof step 107 from proof rg2-lem2-term-unfair (previous step)

□ (N = N' ∧ ¬ N' < N''), [:S | Boolvar ::- [PL N = n20 ∧ S = s20 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s21 ∧ N = n21 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), INDHYP-nat(n20 + 1) ∧ INDHYP-nat0(n2), N = n20 + 1, R2(pm, s3, S), R1(pm, s3, S), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, s3), I(pm, s2), R1(pm, s2, S), I(pm, s21), I(pm, S), I(pm, s20), R1(pm, s2, s3), R2(pm, s2, s2), n21 ≤ n20 + 1, R2(pm, s3, s21), G2(pm, s2, s3), R1(pm, s2, s20), G1(pm, s2, s2), I(pm, s), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4 ⊦ [:S | Boolvar ::- [PL N = n20 ∧ N' = N'' + 1 until last ∧ 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)] ], ◇ last

User applied rule decompose

And closed the goal!

Rule argument

positions: 2, 1

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