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Proof step 8 from proof hasSharing-put-index-refval (previous step)

(st[st[r -- sks] .refval -- i ', refval(r2)][r -- (sks + i ' ' + sks2)]) = refval(r3), st[r -- (sks + i ' ' + sks2)] = refval(st[r -- sks] .refval), (st[st[r -- sks] .refval -- i ', refval(r2)][r -- ((sks + i ' ' + sks2) + i ' ' + sks3)]) = refval(r1), st[st[r -- sks] .refval -- _type] .type = mkarraytype(ty), (st[st[r -- sks] .refval -- i ', refval(r2)][r -- sks0]) = refval(r1), fits(r, sks0, st[st[r -- sks] .refval -- i ', refval(r2)]), fits(r3, i ' ' + sks3, st[st[r -- sks] .refval -- i ', refval(r2)]), fits(r, sks + i ' ' + sks2, st[st[r -- sks] .refval -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ st[r -- sks] .refval = jvmref, r = r2, r1 = jvmref, sks0 = [], sks0 = (sks + i ' ' + sks2) + i ' ' + sks3, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks + i ' ' + sks2 → st[r -- sks0] .refval ≠ st[r -- sks] .refval)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
st[r -- sks] = refval(r0) ∧ is_referencevalue(st[r -- sks]), (st[r0 -- i ', refval(r2)][r -- (sks + i ' ' + sks2)]) = refval(r3), st[r -- (sks + i ' ' + sks2)] = refval(r0), (st[r0 -- i ', refval(r2)][r -- ((sks + i ' ' + sks2) + i ' ' + sks3)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), fits(r, sks0, st[r0 -- i ', refval(r2)]), fits(r3, i ' ' + sks3, st[r0 -- i ', refval(r2)]), fits(r, sks + i ' ' + sks2, st[r0 -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], sks0 = (sks + i ' ' + sks2) + i ' ' + sks3, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ r0), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks + i ' ' + sks2 → st[r -- sks0] .refval ≠ r0)

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[r -- sks], r0] 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], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r -- sks], r0)]]