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Proof step 163 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n41 ∧ S = s41 ∧ N' = N'' + 1 until last] ∥nf false ::- [PL S = s40 ∧ N = n40 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n2 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar, INDHYP-nat(n41 + 1) ∧ INDHYP-nat0(n2), 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 ≤ n41 + 1, I(pm, s), G2(pm, s2, s2), R2(pm, s2, s40), G1(pm, s2, s3), n40 ≤ n41 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s40), I(pm, S), ¬ R1(pm, s3, s41), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n2 = n4 ⊦ ◇ last

User applied rule insert lemma

And obtained the following new goals

Proof step 164:
[:S | [PL S = s] ∥nf [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s1, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), R1(pm, s0, S), ¬ R1(pm, s0, s), Pre2(pm, s1), I(pm, s0) ⊦ ◇ last
Proof step 165:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n41 ∧ S = s41 ∧ N' = N'' + 1 until last] ∥nf false ::- [PL S = s40 ∧ N = n40 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n2 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar, INDHYP-nat(n41 + 1) ∧ INDHYP-nat0(n2), 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 ≤ n41 + 1, I(pm, s), G2(pm, s2, s2), R2(pm, s2, s40), G1(pm, s2, s3), n40 ≤ n41 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s40), I(pm, S), ¬ R1(pm, s3, s41), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n2 = n4 ⊦ [:S | [PL S = s41] ∥nf [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)]], ◇ last

Rule argument

spec: inst: name: rg-blocked1-not-r1-term-unfair seq: [:S | [PL S = s] ∥nf [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s1, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last) ] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), R1(pm, s0, S), ¬ R1(pm, s0, s), Pre2(pm, s1), I(pm, s0) ⊦ ◇ last subst: [S, s, Post2, pm, s1, G2, R2, R1, G1, Pre1, Post1, I, Pre2, s0] → [S, s41, Post2, pm, s, G2, R2, R1, G1, Pre1, Post1, I, Pre2, s3] flags: current, []

Additional information

Used terms: S, s41, Post2, pm, s, G2, R2, R1, G1, Pre1, Post1, I, Pre2, s3