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Proof step 269 from proof hasSharing-put-index-refval (previous step)

validreflist(str, mkjavavalues(r0 ' + r2 '), mkclasstype(`java.lang.Object' .class), st), st[r0 -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r2 -- (sks + i ' ' + sks1)]) = refval(r1), st[r2 -- sks] = refval(r0), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks0, st), validref(str, r2, ty, st), ∀ r1, sks1, r, sks2. ¬ ( r1 ∈ r0 ' + r2 ' ∧ r ∈ r0 ' + r2 ' ∧ r1 ≠ r ∧ fits(r1, sks1, st) ∧ fits(r, sks2, st) ∧ st[r1 -- sks1] = st[r -- sks2] ∧ st[r1 -- sks1] .refval ≠ jvmref), fits(r2, sks, st), fits(r2, sks1, st[r0 -- i ', refval(r2)]) ⊦ sks0 = [], r1 = jvmref, r0 = r2, r0 = jvmref, sks0 = i ' ' + sks + i ' ' + sks1, r2 = jvmref, hasSharing(r0, st), hasSharing(r2, st), junkref(str, r0, st), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r0 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r0 -- sks3] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r0), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r2 -- sks3] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ st[r2 -- sks3] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 268:
st[r0 -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r2 -- (sks + i ' ' + sks1)]) = refval(r1), st[r2 -- sks] = refval(r0), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks0, st), validref(str, r2, ty, st), fits(r2, sks, st), fits(r2, sks1, st[r0 -- i ', refval(r2)]), validref(str, r0, mkclasstype(`java.lang.Object' .class), st), validref(str, r2, mkclasstype(`java.lang.Object' .class), st), ∀ r, sks2, r3, sks3. r ≠ r0 ∧ r ≠ r2 ∨ r3 ≠ r0 ∧ r3 ≠ r2 ∨ r = r3 ∨ ¬ fits(r, sks2, st) ∨ ¬ fits(r3, sks3, st) ∨ st[r -- sks2] ≠ st[r3 -- sks3] ∨ st[r -- sks2] .refval = jvmref ⊦ sks0 = [], r1 = jvmref, r0 = r2, r0 = jvmref, sks0 = i ' ' + sks + i ' ' + sks1, r2 = jvmref, hasSharing(r0, st), hasSharing(r2, st), junkref(str, r0, st), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r0 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r0 -- sks3] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r0), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r2 -- sks3] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ st[r2 -- sks3] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-17, ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : junkrefs, , validreflist-one-01, ⊦ validreflist (str, refval(r) ', ty, st) ↔ validref(str, r, ty, st)], [CSIMPNAMEDSEQ : junkrefs, , validreflist-rec-01, ⊦ validreflist (str, refval(r) ' + vals, ty, st) ↔ validref(str, r, ty, st) ∧ validreflist (str, vals, ty, st)], [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)])]]