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Proof step 721 from proof hasSharing-put-index-refval (previous step)

¬ ¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r2 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ r0)), (st[r0 -- i ', refval(r2)][r2 -- sks0]) = refval(r3), st[r2 -- sks0] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r -- sks1] = refval(r0), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), fits(r4, sks3, st[r0 -- i ', refval(r2)]), fits(r2, sks0, st), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, is_arraytype(st[r3 -- _type] .type) → i < st[r3 -- _length] .intval ⊦ r3 = jvmref, r2 = jvmref, r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks1 = [], is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r2 -- sks2] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks2 → st[r2 -- sks5] .refval ≠ st[r2 -- sks2] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ r0), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 720:
st[r -- sks1] = refval(st[r2 -- sks4] .refval), st[r -- sks] = refval(r1), st[st[r2 -- sks4] .refval -- _type] .type = mkarraytype(ty), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r2 -- (sks4 + i ' ' + sks2)]) = refval(r3), st[r2 -- (sks4 + i ' ' + sks2)] = refval(st[r2 -- sks4] .refval), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r2 -- (sks4 + (i ' ' + sks2) + i ' ' + sks3)]) = refval(r1), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[st[r2 -- sks4] .refval -- _length] .intval, 0 ≤ i, fits(r4, sks3, st[st[r2 -- sks4] .refval -- i ', refval(r2)]), fits(r2, sks4 + i ' ' + sks2, st), 0 < st[st[r2 -- sks4] .refval -- _length] .intval, is_arraytype(st[r3 -- _type] .type) → i < st[r3 -- _length] .intval, ∀ sks0. sks0 + i ' ' ⊑ sks4 → st[r2 -- sks0] .refval ≠ st[r2 -- sks4] .refval ⊦ sks1 = [], r3 = jvmref, r2 = jvmref, st[r2 -- sks4] .refval = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks4 + (i ' ' + sks2) + i ' ' + sks3 = sks, is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = st[r2 -- sks4] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ st[r2 -- sks4] .refval), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = st[r2 -- sks4] .refval ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks0, sks6. sks4 + i ' ' + sks2 = sks0 + i ' ' + sks6 ∧ st[r2 -- sks0] .refval = st[r2 -- sks4] .refval ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r2 -- sks5] .refval ≠ st[r2 -- sks0] .refval), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks4 + i ' ' + sks2 → st[r2 -- sks0] .refval ≠ st[r2 -- sks4] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : list, storekeys, Last, ⊦ sks + sk = sks + sk '], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]