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Proof step 69 from proof rg2-lem2-term-unfair (previous step)

N0 = N0'' + 1 until Boolvar0, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar0 ∨ Boolvar ::- [PL N = n13 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s5 ∧ N = n4 ∧ □ ¬ 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(n13 + 1) ∧ INDHYP-nat0(n2)) ∧ INDHYP-nat1(N0 + 1), N = n13 + 1, R2(pm, s3, S), R1(pm, s3, S), I(pm, s2), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s3), R1(pm, s2, S), I(pm, s5), I(pm, S), R1(pm, s2, s3), n4 ≤ n13 + 1, R2(pm, s3, s5), G2(pm, s2, s3), I(pm, s) ⊦ ◇ last, [:S | Boolvar0 ∨ Boolvar ::- [PL N = n13 ∧ 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)] ]

User applied rule decompose

And closed the goal!

Rule argument

positions: 3, 2

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