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Proof step 729 from proof hasSharing-put-index-refval (previous step)

¬ validreflist(str, mkjavavalues(r ' + r4 '), mkclasstype(`java.lang.Object' .class), st), st[r3 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r3), (st[r3 -- i ', refval(r4)][r4 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r4 -- sks0] = refval(r3), 0 < st[r3 -- _length] .intval, 0 ≤ i, i < st[r3 -- _length] .intval, validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r4, sks0, st), fits(r4, sks3, st[r3 -- i ', refval(r4)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r4, r3 = jvmref, r4 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r3 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r3), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r4 -- sks4] .refval ≠ r3), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r4 -- sks2] .refval = r3 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks2 → st[r4 -- sks5] .refval ≠ st[r4 -- sks2] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 728:
st[r3 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r3), (st[r3 -- i ', refval(r4)][r4 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r4 -- sks0] = refval(r3), 0 < st[r3 -- _length] .intval, 0 ≤ i, i < st[r3 -- _length] .intval, validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r4, sks0, st), fits(r4, sks3, st[r3 -- i ', refval(r4)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r4, r3 = jvmref, r4 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), validreflist(str, refval(r) ' + refval(r4) ', mkclasstype(`java.lang.Object' .class), st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r3 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r3), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r4 -- sks4] .refval ≠ r3), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r4 -- sks2] .refval = r3 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks2 → st[r4 -- sks5] .refval ≠ st[r4 -- sks2] .refval)

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)])]]