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Proof step 55 from proof put-switch-primval-index-index (previous step)

st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + i0 ' ', st), fits(r0, sks, st), fits(r2, i ' ', st), r2 ≠ r1 ∨ i ≠ i0, r1 ≠ r2 ∨ i0 ≠ i ⊦ (st[r2 -- i ', val0][r1 -- i0 ', val]) = (st[r2 -- i ', val0][(st[r2 -- i ', val0][r -- sks1]) .refval -- i0 ', val]), sks = [], is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + i0 ' ')]), is_referencevalue(st[r0 -- (sks + i ' ')]), junkref(str, r, st), junkref(str, r0, st), junkref(str, r1, st), is_referencevalue(st[r1 -- i0 '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ fits(r, sk ', st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval)
Proof step 54:
st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + i0 ' ', st), fits(r0, sks, st), r2 ≠ jvmref ∧ is_referencevalue(st[r2 -- i ']) ∧ (is_classtype(st[r2 -- _type] .type) → i ' ∈ instfields(st[r2 -- _type] .type .class)) ∧ (is_arraytype(st[r2 -- _type] .type) → is_indexkey(i ') ∧ 0 ≤ i ' .index ∧ i ' .index < st[r2 -- _length] .intval), r2 ≠ r1 ∨ i ≠ i0, r1 ≠ r2 ∨ i0 ≠ i ⊦ (st[r2 -- i ', val0][r1 -- i0 ', val]) = (st[r2 -- i ', val0][(st[r2 -- i ', val0][r -- sks1]) .refval -- i0 ', val]), sks = [], is_referencevalue(val), is_referencevalue(val0), is_referencevalue(st[r -- (sks1 + i0 ' ')]), is_referencevalue(st[r0 -- (sks + i ' ')]), junkref(str, r, st), junkref(str, r0, st), junkref(str, r1, st), is_referencevalue(st[r1 -- i0 '])

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-storekeys-one antecedent: succedent: fits(r, sk ', st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ ( is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) substlist: [st, sk, r] → [st, i ', r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i ', r2)]]