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Proof step 33 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), (r ∈ rs1 → g(r) = a) ∧ (r0 ∈ rs0 → g(r0) = a)

User applied rule case distinction

And obtained the following new goals

Proof step 34:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), r ∈ rs1, ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ g(r) = a, ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g))
Proof step 36:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), r0 ∈ rs0, ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ g(r0) = a, ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g))

Rule argument

pos: right 2

Proof step 33 from proof embed-split (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information