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Proof step 22 from proof eqex-tput (previous step)

eqex(st0[r -- sk, val], st1, r1), eqex(st1, st0[r -- sk, val], r1), eqex(st0, st, r1), eqex(st, st0, r1), ∀ rk. (rk ∈ st -- r1 ↔ rk ∈ st0 -- r1) ∧ (st -- r1)[rk] = (st0 -- r1)[rk], ∀ rk0. (rk0 ∈ st0[r -- sk, val] -- r1 ↔ rk0 ∈ st1 -- r1) ∧ (st0[r -- sk, val] -- r1)[rk0] = (st1 -- r1)[rk0] ⊦ ∅[r1 -- sk0] = (st1 -- r1)[r1 -- sk0], r1 -- sk0 ∈ st[r -- sk, val] -- r1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,¬ rk ∈ st → st[rk] = ∅[rk] ,[rk, st] → [r1 -- sk0, st1 -- r1] ,F ,store ,javastore ,notmemlookup ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk ∈ st -- r0 ↔ r ≠ r0 ∧ r -- sk ∈ st])], [EXTRATERMS : (r1 -- sk0, st1 -- r1)]]