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Proof step 405 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 404:
(st[st[r3 -- sks3] .refval -- i ', refval(r3)][r3 -- (sks3 + i ' ' + sks4)]) = refval(r2), st[r3 -- (sks3 + i ' ' + sks4)] = refval(st[r3 -- sks3] .refval), st[r3 -- sks2] = refval(r1), st[st[r3 -- sks3] .refval -- _type] .type = mkarraytype(ty), (st[st[r3 -- sks3] .refval -- i ', refval(r3)][r3 -- ((sks3 + i ' ' + sks4) + i ' ' + sks0)]) = refval(r1), st[r -- sks1] = refval(st[r3 -- sks3] .refval), validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), fits(r2, i ' ' + sks0, st[st[r3 -- sks3] .refval -- i ', refval(r3)]), fits(r3, sks3 + i ' ' + sks4, st[st[r3 -- sks3] .refval -- i ', refval(r3)]), i < st[st[r3 -- sks3] .refval -- _length] .intval, 0 ≤ i, is_referencevalue(st[st[r3 -- sks3] .refval -- i ', refval(r3)][st[r3 -- sks3] .refval -- (i ' ' + (sks3 + i ' ' + sks4) + i ' ' + sks0)]), fits(r3, sks2, st), is_referencevalue(st[st[r3 -- sks3] .refval -- i ', refval(r3)][st[r3 -- sks3] .refval -- (i ' ' + sks2)]), 0 < st[st[r3 -- sks3] .refval -- _length] .intval ⊦ sks2 = (sks3 + i ' ' + sks4) + i ' ' + sks0, r1 = jvmref, r = r3, st[r3 -- sks3] .refval = jvmref, sks1 = [], r3 = jvmref, hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks5. ¬ (sks5 + i ' ' ⊑ sks3 → st[r3 -- sks5] .refval ≠ st[r3 -- sks3] .refval), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks3 + i ' ' + sks4 → st[r3 -- sks0] .refval ≠ st[r3 -- sks3] .refval), ∃ sks1, sks0. sks2 = sks1 + i ' ' + sks0 ∧ st[r3 -- sks1] .refval = st[r3 -- sks3] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r3 -- sks4] .refval ≠ st[r3 -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r3 -- sks3] .refval), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = st[r3 -- sks3] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r3 -- sks3] .refval), ∃ sks0, sks4. sks1 = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = st[r3 -- sks3] .refval ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : specialkeys, , len, ⊦ _length ≠ i '], [CSIMPNAMEDSEQ : specialkeys, , type-03, ⊦ _type ≠ i '], [CSIMPNAMEDSEQ : list, storekeys, Last, ⊦ sks + sk = sks + sk '], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]