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Proof step 4 from proof seq-sat-rg (previous step)

(∃ Out0. [:S, Out0 | SEQ#(m, Inpf(m); S, Out0)] ∧ □ (Out0 = Outf(m) ∧ Out0' = Outf'(m))) → (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S);(Gr(m)(S, S') ∧ ¬ blocked) ∧ (GInv(S) → GInv(S'))), □ Inpf = Inpf', [:S, Outf | SEQ#(m, Inpf(m); S, Outf(m))], GInv(S), Pr(m)(S) ⊦ (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

User applied rule case distinction

And obtained the following new goals

Proof step 5:
[:S, Outf | SEQ#(m, Inpf(m); S, Outf(m))], □ Inpf = Inpf', GInv(S), Pr(m)(S) ⊦ (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), ∃ Out0. [:S, Out0 | SEQ#(m, Inpf(m); S, Out0)] ∧ □ (Out0 = Outf(m) ∧ Out0' = Outf'(m))
Proof step 13:
□ Inpf = Inpf', (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S);(Gr(m)(S, S') ∧ ¬ blocked) ∧ (GInv(S) → GInv(S'))), [:S, Outf | SEQ#(m, Inpf(m); S, Outf(m))], GInv(S), Pr(m)(S) ⊦ (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

Rule argument

pos: left 1

Proof step 4 from proof seq-sat-rg (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information