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Proof step 76 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g], a[r => o1][rs1, f(r; o1), g], R[rs0, f(r; o1), g], ∀ r. r ∈ rs1 → g(r) = a, ∀ r0. (r0 ∈ rs1 → r0 = r) ∧ (r0 ∈ rs1 → f(r0) = (r0 = r ⊃ o0;(∅ ++ r)[r0])) ⊦ f(r) = o0, r = null

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: r abort: F discard: F computed: T

Additional information

Used simplifier rules: map-in0: ⊦ a[r => o][rs, f, g] → r ∈ rs; Used terms: r