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Proof step 39 from proof hasSharing-put-index-refval (previous step)

¬ validreflist(str, mkjavavalues(r ' + r2 '), mkclasstype(`java.lang.Object' .class), st), (st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), st[r2 -- sks] = refval(r), (st[r -- i ', refval(r2)][r2 -- (sks + i ' ' + sks0)]) = refval(r2), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r0 -- i ']) = refval(r1), fits(r1, sks0, st[r -- i ', refval(r2)]), fits(r2, sks, st), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), 0 ≤ i, i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r0 = jvmref, r2 = jvmref, r = r2, r = jvmref, is_classtype(st[r0 -- _type] .type), hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r2 -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r2 -- sks2] .refval ≠ st[r2 -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
(st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), st[r2 -- sks] = refval(r), (st[r -- i ', refval(r2)][r2 -- (sks + i ' ' + sks0)]) = refval(r2), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r0 -- i ']) = refval(r1), fits(r1, sks0, st[r -- i ', refval(r2)]), fits(r2, sks, st), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), 0 ≤ i, i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r0 = jvmref, r2 = jvmref, r = r2, r = jvmref, is_classtype(st[r0 -- _type] .type), hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), validreflist(str, refval(r) ' + refval(r2) ', mkclasstype(`java.lang.Object' .class), st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r2 -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r2 -- sks2] .refval ≠ st[r2 -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : valuesfuns, , mkvalsr-one, ⊦ mkjavavalues(r ') = refval(r) '], [CSIMPNAMEDSEQ : valuesfuns, , mkvalsr-rec, ⊦ mkjavavalues(r ' + refs) = refval(r) ' + mkjavavalues(refs)])]]