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Proof step 4 from proof del-subset-del (previous step)

rk ∈ st -- r ⊦ rk ∈ st -- (r -- sk) ∧ (st -- r)[rk] = (st -- (r -- sk))[rk]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ r -- sk ∈ st -- r0 ↔ r ≠ r0 ∧ r -- sk ∈ st
Proof step 3:
⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]

Rule argument

[VARWITHVARSEQSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;], [CSIMPSEQ : ⊦ rk ∈ st -- rk0 ↔ rk ≠ rk0 ∧ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- (r -- sk))[r0 -- sk0] = st[r0 -- sk0]])]]