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Proof step 2 from proof spawn-rg-total-correct-strng (previous step)

[:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S) ⊦ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);(Gton(n)(S, S') ∧ ¬ blocked) ∧ (GInv(S) → GInv(S'))) ∧ (□ (Rton(n)(S', S'') ∧ GInv(S) ∧ GInv(S')) → ◇ last)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
[:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S) ⊦ (□ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) → ◇ last) ∧ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);Gton(n)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))
Proof step 4:
(Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);Gton(n)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), □ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) → ◇ last, [:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S) ⊦ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);(Gton(n)(S, S') ∧ ¬ blocked) ∧ (GInv(S) → GInv(S'))) ∧ (□ (Rton(n)(S', S'') ∧ GInv(S) ∧ GInv(S')) → ◇ last)

Rule argument

spec: inst: name: spawn-sat-rg+df+term seq: [:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S) ⊦ (□ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) → ◇ last) ∧ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S) ;Gton(n)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')) ) subst: [Inpf, S, Outf, n] → [Inpf, S, Outf, n] flags: current, []

Additional information

Used terms: Inpf, S, Outf, n