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Proof step 11 from proof mod-other-hp2 (previous step)

rs2 ∩ rs = ∅, rs1 ∩ rs2 = ∅, rs1 ∩ rs = ∅, a0[P0][rs2, f, g], R[rs, f, g], a[P][rs1, f, g] ⊦ g(r) = a0, g(r) = a, (a[P] * a0[P0] * true)[rs1 ∪ rs2 ∪ rs, f(r; o), g], a[P][rs1, f(r; o), g] ∧ (a0[P0] * true)[rs2 ∪ rs, f(r; o), g]

User applied rule case distinction

And obtained the following new goals

Proof step 12:
rs1 ∩ rs = ∅, rs1 ∩ rs2 = ∅, rs2 ∩ rs = ∅, a[P][rs1, f, g], R[rs, f, g], a0[P0][rs2, f, g] ⊦ g(r) = a, g(r) = a0, (a[P] * a0[P0] * true)[rs1 ∪ rs2 ∪ rs, f(r; o), g], a[P][rs1, f(r; o), g]
Proof step 27:
rs1 ∩ rs = ∅, rs1 ∩ rs2 = ∅, rs2 ∩ rs = ∅, a[P][rs1, f, g], R[rs, f, g], a0[P0][rs2, f, g] ⊦ g(r) = a, g(r) = a0, (a[P] * a0[P0] * true)[rs1 ∪ rs2 ∪ rs, f(r; o), g], (a0[P0] * true)[rs2 ∪ rs, f(r; o), g]

Rule argument

pos: right 4

Proof step 11 from proof mod-other-hp2 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information