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Proof step 179 from proof rg2-lem1-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n44 ∧ S = s55 ∧ 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 = n43 ∧ S = s54 ∧ □ ¬ N' < N'' ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n44 = N ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n44 + 1) ∧ INDHYP-nat0(n44 + 1), R2(pm, s2, S), I(pm, s3), I(pm, s2), 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), N ≤ n44 + 1, I(pm, s), G2(pm, s2, s2), G1(pm, s2, s3), R1(pm, s3, s55), n43 ≤ n44 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s55), I(pm, S), ¬ R2(pm, s2, s54), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ ◇ last

User applied rule insert lemma

And obtained the following new goals

Proof step 180:
[:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s1, S);G1(pm, S, S')) ∧ (□ R1(pm, S', S'') → ◇ last)] ∥nf [PL S = s]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), R2(pm, s0, S), ¬ R2(pm, s0, s), Pre1(pm, s1), I(pm, s0) ⊦ ◇ last
Proof step 181:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n44 ∧ S = s55 ∧ 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 = n43 ∧ S = s54 ∧ □ ¬ N' < N'' ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n44 = N ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n44 + 1) ∧ INDHYP-nat0(n44 + 1), R2(pm, s2, S), I(pm, s3), I(pm, s2), 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), N ≤ n44 + 1, I(pm, s), G2(pm, s2, s2), G1(pm, s2, s3), R1(pm, s3, s55), n43 ≤ n44 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s55), I(pm, S), ¬ R2(pm, s2, s54), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ (□ R1(pm, S', S'') → ◇ last)] ∥nf [PL S = s54]], ◇ last

Rule argument

spec: inst: name: rg-blocked2-not-r2-term-unfair seq: [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s1, S);G1(pm, S, S')) ∧ (□ R1(pm, S', S'') → ◇ last) ] ∥nf [PL S = s] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), R2(pm, s0, S), ¬ R2(pm, s0, s), Pre1(pm, s1), I(pm, s0) ⊦ ◇ last subst: [Post1, pm, s1, S, G1, R1, s, R2, Pre1, I, G2, Pre2, Post2, s0] → [Post1, pm, s, S, G1, R1, s54, R2, Pre1, I, G2, Pre2, Post2, s2] flags: current, []

Additional information

Used terms: Post1, pm, s, S, G1, R1, s54, R2, Pre1, I, G2, Pre2, Post2, s2