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Proof step 42 from proof put-switch-primval-index-field (previous step)

st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + i ' ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r1 -- i ', val][(st[r1 -- i ', val][r0 -- sks]) .refval -- mkfs(class, ty, fieldvar) ', val0]) = (st[r2 -- mkfs(class, ty, fieldvar) ', val0][(st[r2 -- mkfs(class, ty, fieldvar) ', val0][r -- sks1]) .refval -- i ', val]), junkref(str, r0, st), junkref(str, r, st), is_reftype(ty), is_referencevalue(st[r -- (sks1 + i ' ')]), is_referencevalue(val0), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ sk ∈ sks ∧ sks ≠ [] → (st[r -- sk, val][r0 -- sks]) = st[r0 -- sks]
Proof step 16:
¬ (¬ mkfs(class, ty, fieldvar) ' ∈ sks1 ∧ sks1 ≠ []), st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + i ' ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r1 -- i ', val][(st[r1 -- i ', val][r0 -- sks]) .refval -- mkfs(class, ty, fieldvar) ', val0]) = (st[r2 -- mkfs(class, ty, fieldvar) ', val0][(st[r2 -- mkfs(class, ty, fieldvar) ', val0][r -- sks1]) .refval -- i ', val]), junkref(str, r0, st), junkref(str, r, st), is_reftype(ty), is_referencevalue(st[r -- (sks1 + i ' ')]), is_referencevalue(val0), is_referencevalue(val)
Proof step 41:
¬ mkfs(class, ty, fieldvar) ' ∈ sks1 ∧ sks1 ≠ [], st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), fits(r, sks1 + i ' ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r1 -- i ', val][(st[r1 -- i ', val][r0 -- sks]) .refval -- mkfs(class, ty, fieldvar) ', val0]) = (st[r2 -- mkfs(class, ty, fieldvar) ', val0][st[r -- sks1] .refval -- i ', val]), junkref(str, r0, st), junkref(str, r, st), is_reftype(ty), is_referencevalue(st[r -- (sks1 + i ' ')]), is_referencevalue(val0), is_referencevalue(val)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: at-put-other-02 antecedent: succedent: ¬ sk ∈ sks ∧ sks ≠ [] → (st[r -- sk, val][r0 -- sks]) = st[r0 -- sks] substlist: [sks, r0, val, sk, r, st] → [sks1, r, val0, mkfs(class, ty, fieldvar) ', r2, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks1, r, val0, mkfs(class, ty, fieldvar) ', r2, st)]]