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Proof step 27 from proof mod-other-hp2 (previous step)

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]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ g(r) ≠ a ∧ (a[P] * R)[rs, f, g] → (a[P] * true)[rs, f(r; o), g]
Proof step 29:
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, (a0[P0] * true)[rs2 ∪ rs, f(r; o), g], (a[P] * a0[P0] * true)[rs1 ∪ rs2 ∪ rs, f(r; o), g], g(r) ≠ a0 ∧ (a0[P0] * true)[rs2 ∪ rs, f, g]

Rule argument

spec: <toplevel> name: mod-other-hp seq: ⊦ g(r) ≠ a ∧ (a[P] * R)[rs, f, g] → (a[P] * true)[rs, f(r; o), g] subst: [R, g, o, r, f, rs, P, a] → [true, g, o, r, f, rs2 ∪ rs, P0, a0] flags: <all paths>

Additional information

Used terms: true, g, o, r, f, rs2 ∪ rs, P0, a0