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Proof step 21 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g], ((r => o1))(mk(rs1, f(r; o1))) ∧ (r0 ∈ rs1 → g(r0) = a)

User applied rule case distinction

And obtained the following new goals

Proof step 22:
rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ ((r => o1))(mk(rs1, f(r; o1))), (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g]
Proof step 35:
rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], r0 ∈ rs1, ∀ r. r ∈ rs1 → g(r) = a ⊦ g(r0) = a, (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g]

Rule argument

pos: right 2

Proof step 21 from proof write-known (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information