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Proof step 18 from proof put-switch-primval-field-field (previous step)

st[r -- sks1] = refval(r1), fits(r2, mkfs(class0, ty0, fieldvar0) ' ', st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), r1 ≠ r2 ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0, r2 ≠ r1 ∨ class0 ≠ class ∨ ty0 ≠ ty ∨ fieldvar0 ≠ fieldvar ⊦ sks1 = [], (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r1 -- mkfs(class, ty, fieldvar) ', val]) = (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0] [(st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r -- sks1]) .refval -- mkfs(class, ty, fieldvar) ', val ] ), junkref(str, r2, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), is_referencevalue(val0), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ sk ∈ sks ∧ sks ≠ [] → (st[r -- sk, val][r0 -- sks]) = st[r0 -- sks]
Proof step 17:
¬ (¬ mkfs(class0, ty0, fieldvar0) ' ∈ sks1 ∧ sks1 ≠ []), st[r -- sks1] = refval(r1), fits(r2, mkfs(class0, ty0, fieldvar0) ' ', st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), r1 ≠ r2 ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0, r2 ≠ r1 ∨ class0 ≠ class ∨ ty0 ≠ ty ∨ fieldvar0 ≠ fieldvar ⊦ sks1 = [], (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r1 -- mkfs(class, ty, fieldvar) ', val]) = (st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0] [(st[r2 -- mkfs(class0, ty0, fieldvar0) ', val0][r -- sks1]) .refval -- mkfs(class, ty, fieldvar) ', val ] ), junkref(str, r2, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), 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(class0, ty0, fieldvar0) ', r2, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (sks1, r, val0, mkfs(class0, ty0, fieldvar0) ', r2, st)]]