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Proof step 3 from proof rely-map-write-known (previous step)

(a[r => o] * R)[rs, f, g], r0 ∈ rs ⊦ # rs = 0, a = g(r0), f(r0) = (r = r0 ⊃ o0;f(r0)), rs = ∅

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 3

Additional information

Used simplifier rules: sep-ass: ⊦ (R0 * R1) * R2 = R0 * R1 * R2; from specification heap-sep[heap-aux]%sep-com: ⊦ R0 * R1 = R1 * R0; from specification heap-sep[heap-aux]% ⊦ (a[r => o] * R)[rs, f, g] → (g(r) = a ↔ true); (ss)