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Proof step 454 from proof hasSharing-put-index-refval (previous step)

¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r -- sks0] .refval = r2 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r2)), (st[r2 -- i ', refval(r3)][st[r -- sks] .refval -- (i ' ' + sks2)]) = refval(r1), st[r2 -- _type] .type = mkarraytype(ty), (st[r2 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r -- sks1] = refval(r2), st[r -- sks] = refval(r2), 0 < st[r2 -- _length] .intval, validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), fits(r3, sks3, st[r2 -- i ', refval(r3)]), i < st[r2 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r2 -- i ', refval(r3)][r2 -- (i ' ' + sks3)]), fits(r, sks, st), fits(r3, sks2, st[r2 -- i ', refval(r3)]), r3 = jvmref → is_reftype(ty) ⊦ sks1 = [], sks + i ' ' + sks2 = sks1 + i ' ' + sks3, r1 = jvmref, r = r3, r2 = jvmref, sks = [], hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r2), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = r2 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ r2), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r2 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 453:
st[r -- sks] = refval(r2), st[r -- sks1] = refval(r2), (st[r2 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r2 -- _type] .type = mkarraytype(ty), (st[r2 -- i ', refval(r3)][r2 -- (i ' ' + sks2)]) = refval(r1), fits(r3, sks2, st[r2 -- i ', refval(r3)]), fits(r, sks, st), is_referencevalue(st[r2 -- i ', refval(r3)][r2 -- (i ' ' + sks3)]), 0 ≤ i, i < st[r2 -- _length] .intval, fits(r3, sks3, st[r2 -- i ', refval(r3)]), fits(r, sks1, st), disjoint(str, r ' + r3 ', st), validref(str, r3, ty, st), 0 < st[r2 -- _length] .intval, r3 = jvmref → is_reftype(ty) ⊦ sks = [], r2 = jvmref, r = r3, r1 = jvmref, sks + i ' ' + sks2 = sks1 + i ' ' + sks3, sks1 = [], junkref(str, r, st), hasSharing(r3, st), hasSharing(r, st), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r2 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ r2), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = r2 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r2)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, storekeys, Last, ⊦ sks + sk = sks + sk '], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]