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Proof step 56 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], r ∈ rs0, ∀ r. r ∈ rs1 → g(r) = a ⊦ # rs0 = 0, rs0 = ∅, R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], r ∈ rs0, ∀ r. r ∈ rs1 → g(r) = a ⊦ # rs0 = 0, rs0 = ∅, R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

Proof step 56 from proof write-known (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information