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Proof step 8 from proof spawn-sat-rg-strnger (previous step)

□ Inpf = Inpf', Pr(0)(S) → (Ry(0)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(0)(S) ∧ GInv(S);Gr(0)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), Prton(0)(S), GInv(S) ⊦ (Rton(0)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(0)(S) ∧ GInv(S);Gton(0)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

User applied rule case distinction

And obtained the following new goals

Proof step 9:
□ Inpf = Inpf', Prton(0)(S), GInv(S), ¬ Pr(0)(S) ⊦ (Rton(0)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(0)(S) ∧ GInv(S);Gton(0)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))
Proof step 11:
□ Inpf = Inpf', (Ry(0)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(0)(S) ∧ GInv(S);Gr(0)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), Prton(0)(S), GInv(S) ⊦ (Rton(0)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(0)(S) ∧ GInv(S);Gton(0)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

Rule argument

pos: left 2

Proof step 8 from proof spawn-sat-rg-strnger (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information