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Proof step 19 from proof put-switch-primval-index-index (previous step)

st[r -- sks1] = refval(r1), fits(r2, sk0 ', st), fits(r, sks1 + sk ', st), is_indexkey(sk0), is_indexkey(sk), r1 ≠ r2 ∨ sk ≠ sk0 ⊦ (st[r1 -- sk, val][r2 -- sk0, val0]) = (st[r2 -- sk0, val0][(st[r2 -- sk0, val0][r -- sks1]) .refval -- sk, val]), is_referencevalue(st[r2 -- sk0]), junkref(str, r, st), junkref(str, r2, st), is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + sk ')])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 18:
r2 -- sk0 ≠ r1 -- sk, st[r -- sks1] = refval(r1), fits(r2, sk0 ', st), fits(r, sks1 + sk ', st), is_indexkey(sk0), is_indexkey(sk), r1 ≠ r2 ∨ sk ≠ sk0 ⊦ (st[r2 -- sk0, val0][r1 -- sk, val]) = (st[r2 -- sk0, val0][(st[r2 -- sk0, val0][r -- sks1]) .refval -- sk, val]), is_referencevalue(st[r2 -- sk0]), junkref(str, r, st), junkref(str, r2, st), is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + sk ')])

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: rew antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) substlist: [val0, rk, val, rk0, st] → [val0, r2 -- sk0, val, r1 -- sk, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (val0, r2 -- sk0, val, r1 -- sk, st)]]