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Proof step 381 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 349:
⊦ fits(jvmref, sks, st) ↔ sks = []
Proof step 380:
(st[r0 -- i ', refval(r3)][r3 -- sks]) = refval(r2) ∧ is_referencevalue(st[r0 -- i ', refval(r3)][r3 -- sks]), st[r3 -- sks] = refval(r0), (st[r0 -- i ', refval(r3)][r3 -- (sks + i ' ' + sks0)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r -- sks1] = refval(r0), validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), fits(r3, sks3, st[r0 -- i ', refval(r3)]), i < st[r0 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks3)]), fits(r2, i ' ' + sks0, st[r0 -- i ', refval(r3)]), fits(r3, sks, st[r0 -- i ', refval(r3)]), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks + i ' ' + sks0)]), 0 < st[r0 -- _length] .intval ⊦ sks + i ' ' + sks0 = sks3, r1 = jvmref, r = r3, r0 = jvmref, sks1 = [], r3 = jvmref, hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r3 -- sks4] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .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), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ r0), ∃ sks0, sks4. sks1 = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-refval antecedent: is_referencevalue(val) succedent: r = val .refval ↔ val = refval(r) substlist: [val, r] → [st[r0 -- i ', refval(r3)][r3 -- sks], r2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valuefuns, , refval-xtra, ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r0 -- i ', refval(r3)][r3 -- sks], r2)]]