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Proof step 52 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g(r; a1)], a1[r => o][rs1, f, g(r; a1)] ⊦ (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g] ∧ rs1 ∩ rs0 = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
rs1 ∩ rs0 = ∅, a1[r => o][rs1, f, g(r; a1)], R[rs0, f, g(r; a1)] ⊦ (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

Proof step 52 from proof aux-known (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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