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Proof step 524 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 483:
⊦ fits(jvmref, sks, st) ↔ sks = []
Proof step 523:
st[r -- sks1] = refval(st[r4 -- sks] .refval), (st[st[r4 -- sks] .refval -- i ', refval(r4)][r4 -- (sks + i ' ' + sks4)]) = refval(r1), st[st[r4 -- sks] .refval -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), 0 ≤ i, i < st[st[r4 -- sks] .refval -- _length] .intval, fits(r4, sks + i ' ' + sks4, st[st[r4 -- sks] .refval -- i ', refval(r4)]), fits(r, sks1, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), is_referencevalue(st[st[r4 -- sks] .refval -- i ', refval(r4)][st[r4 -- sks] .refval -- (i ' ' + sks + i ' ' + sks4)]), 0 < st[st[r4 -- sks] .refval -- _length] .intval ⊦ st[r4 -- sks] .refval = jvmref, r = r4, r1 = jvmref, sks0 = [], sks0 = sks1 + i ' ' + sks + i ' ' + sks4, sks1 = [], r4 = jvmref, junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ st[r4 -- sks] .refval), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = st[r4 -- sks] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = st[r4 -- sks] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r4 -- sks] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : junkrefs, , validref-null, ⊦ validref(str, jvmref, ty, st)], [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])]]