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Proof step 59 from proof put-switch-primval-index-index (previous step)

st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + sk ', st), is_indexkey(sk0), is_indexkey(sk), fits(r0, sks, st), fits(r2, sk0 ', st), r2 ≠ r1 ∨ sk0 ≠ 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]), sks = [], is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + sk ')]), is_referencevalue(st[r0 -- (sks + sk0 ')]), junkref(str, r, st), junkref(str, r0, st), junkref(str, r1, st), is_referencevalue(st[r1 -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 58:
st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + sk ', st), ∃ i. sk0 = i ', is_indexkey(sk), fits(r0, sks, st), fits(r2, sk0 ', st), r2 ≠ r1 ∨ sk0 ≠ 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]), sks = [], is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + sk ')]), is_referencevalue(st[r0 -- (sks + sk0 ')]), junkref(str, r, st), junkref(str, r0, st), junkref(str, r1, st), is_referencevalue(st[r1 -- sk])

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: ex-04 antecedent: succedent: is_indexkey(sk) ↔ (∃ i. sk = i ') substlist: [sk] → [sk0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk0)]]