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Proof step 631 from proof hasSharing-put-index-refval (previous step)

validreflist(str, mkjavavalues(r ' + r1 '), mkclasstype(`java.lang.Object' .class), st), st[r1 -- sks0] = refval(r), st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), fits(r1, sks0 + i ' ', st[r -- i ', refval(r1)]), fits(r, sks, st), ∀ r0, sks1, r2, sks2. ¬ ( r0 ∈ r ' + r1 ' ∧ r2 ∈ r ' + r1 ' ∧ r0 ≠ r2 ∧ fits(r0, sks1, st) ∧ fits(r2, sks2, st) ∧ st[r0 -- sks1] = st[r2 -- sks2] ∧ st[r0 -- sks1] .refval ≠ jvmref), validref(str, r1, ty, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ i ' ' + sks0 + i ' ' = sks, r = jvmref, r = r1, sks = [], r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r1, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r1 -- sks3] .refval ≠ r), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r1 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r1 -- sks3] .refval ≠ st[r1 -- sks2] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 630:
st[r1 -- sks0] = refval(r), st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), fits(r1, sks0 + i ' ', st[r -- i ', refval(r1)]), fits(r, sks, st), validref(str, r1, ty, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, validref(str, r, mkclasstype(`java.lang.Object' .class), st), validref(str, r1, mkclasstype(`java.lang.Object' .class), st), ∀ r0, sks1, r2, sks2. r0 ≠ r ∧ r0 ≠ r1 ∨ r2 ≠ r ∧ r2 ≠ r1 ∨ r0 = r2 ∨ ¬ fits(r0, sks1, st) ∨ ¬ fits(r2, sks2, st) ∨ st[r0 -- sks1] ≠ st[r2 -- sks2] ∨ st[r0 -- sks1] .refval = jvmref ⊦ i ' ' + sks0 + i ' ' = sks, r = jvmref, r = r1, sks = [], r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r1, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r1 -- sks3] .refval ≠ r), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r1 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r1 -- sks3] .refval ≠ st[r1 -- sks2] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-17, ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : junkrefs, , validreflist-one-01, ⊦ validreflist (str, refval(r) ', ty, st) ↔ validref(str, r, ty, st)], [CSIMPNAMEDSEQ : junkrefs, , validreflist-rec-01, ⊦ validreflist (str, refval(r) ' + vals, ty, st) ↔ validref(str, r, ty, st) ∧ validreflist (str, vals, ty, st)], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : valuesfuns, , mkvalsr-one, ⊦ mkjavavalues(r ') = refval(r) '], [CSIMPNAMEDSEQ : valuesfuns, , mkvalsr-rec, ⊦ mkjavavalues(r ' + refs) = refval(r) ' + mkjavavalues(refs)])]]