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Proof step 65 from proof rg2-lem1-term-unfair (previous step)

□ (N = N' ∧ ¬ N' < N''), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), boolvar ∨ n2 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar0, ¬ boolvar ∧ ¬ boolvar0 ∧ G2(pm, s2, s3) ∧ ¬ n16 + 1 < n ∧ ¬ R2(pm, s3, s0) ∧ ¬ boolvar3 ∧ [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ 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 ∧ S = s0 ∧ □ ¬ N' < N''] ] ∨ ¬ boolvar ∧ ¬ boolvar0 ∧ G2(pm, s2, s3) ∧ ¬ n16 + 1 < n0 ∧ ¬ R2(pm, s3, s1) ∧ ¬ boolvar3 ∧ [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ 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 = n0 ∧ S = s1 ∧ □ ¬ N' < N'' ∧ ¬ □ R2(pm, S', S'')] ] ∨ ¬ boolvar ∧ ¬ boolvar0 ∧ G2(pm, s2, s3) ∧ ¬ n16 + 1 < n1 ∧ ¬ R2(pm, s3, s4) ∧ ¬ boolvar3 ∧ [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ 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 = n1 ∧ S = s4 ∧ □ ¬ N' < N'' ∧ ◇ last] ] ∨ ¬ boolvar ∧ ¬ boolvar0 ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s5) ∧ ¬ n16 + 1 < n3 ∧ ¬ boolvar3 ∧ [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ 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 = s5 ∧ N = n3 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ] ∨ ¬ boolvar ∧ ¬ boolvar0 ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s6) ∧ ¬ n16 + 1 < n5 ∧ ¬ boolvar3 ∧ [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ 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 = s6 ∧ N = n5 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], (INDHYP-nat(n16 + 1) ∧ INDHYP-nat0(n16 + 1)) ∧ INDHYP-nat1(n2), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, s2), R1(pm, s3, S), R2(pm, s3, S), N ≤ n16 + 1, I(pm, s), boolvar3 → s2 = s3 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2) ∧ n2 = n4 ⊦ ◇ last

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 4

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