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Proof step 24 from proof cf-map-unknown (previous step)

cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], ((r => a × r0))(mk(rs1, cf)) ∧ (r1 ∈ rs1 → af(r1) = o)

User applied rule case distinction

And obtained the following new goals

Proof step 25:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ ((r => a × r0))(mk(rs1, cf)), (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af]
Proof step 51:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], r1 ∈ rs1, ∀ r. r ∈ rs1 → af(r) = o ⊦ af(r1) = o, (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af]

Rule argument

pos: right 2

Proof step 24 from proof cf-map-unknown (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information