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Proof step 785 from proof hasSharing-put-index-refval (previous step)

st[r -- sks1] = refval(r0), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), fits((st[r0 -- i ', refval(r2)][r -- sks1]) .refval, i ' ' + sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st[r0 -- i ', refval(r2)]), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 584:
⊦ fits(jvmref, sks, st) ↔ sks = []
Proof step 784:
(st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3) ∧ is_referencevalue(st[r0 -- i ', refval(r2)][r -- sks1]), st[r -- sks1] = refval(r0), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), fits(r3, i ' ' + sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st[r0 -- i ', refval(r2)]), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-refval antecedent: is_referencevalue(val) succedent: r = val .refval ↔ val = refval(r) substlist: [val, r] → [st[r0 -- i ', refval(r2)][r -- sks1], r3] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valuefuns, , refval-xtra, ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r0 -- i ', refval(r2)][r -- sks1], r3)]]