[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 167 from proof rg2-lem1-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n38 ∧ S = s48 ∧ 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 = n37 ∧ S = s47 ∧ □ ¬ N' < N'' ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n38 = N ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n38 + 1) ∧ INDHYP-nat0(n38 + 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 ≤ n38 + 1, I(pm, s), G2(pm, s2, s2), G1(pm, s2, s3), R1(pm, s3, s48), n37 ≤ n38 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s48), I(pm, S), ¬ R2(pm, s2, s47), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ ◇ last

User applied rule insert lemma

And obtained the following new goals

Proof step 168:
[: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 169:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n38 ∧ S = s48 ∧ 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 = n37 ∧ S = s47 ∧ □ ¬ N' < N'' ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n38 = N ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n38 + 1) ∧ INDHYP-nat0(n38 + 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 ≤ n38 + 1, I(pm, s), G2(pm, s2, s2), G1(pm, s2, s3), R1(pm, s3, s48), n37 ≤ n38 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s48), I(pm, S), ¬ R2(pm, s2, s47), 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 = s47]], ◇ 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, s47, R2, Pre1, I, G2, Pre2, Post2, s2] flags: current, []

Additional information

Used terms: Post1, pm, s, S, G1, R1, s47, R2, Pre1, I, G2, Pre2, Post2, s2