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Proof step 32 from proof fits-put-other (previous step)

sk0 ' + sks0 ≠ [], ∀ r, st, r0, sk, val. (fits(r, sks0, st[r0 -- sk, val]) ↔ fits(r, sks0, st)) ∨ sk = _length ∨ sk = _type ∨ (∃ sks2, sks1. sks0 = sks2 + sk ' + sks1 ∧ st[r -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + sk ' ⊑ sks2 → st[r -- sks3] .refval ≠ st[r -- sks2] .refval)) ⊦ sk = _length, sk = _type, r ≠ jvmref ∧ is_referencevalue(st[r0 -- sk, val][r -- (sk0 ' + sks0) .first]) ∧ (is_classtype((st[r0 -- sk, val][r -- _type]) .type) → (sk0 ' + sks0) .first ∈ instfields((st[r0 -- sk, val][r -- _type]) .type .class)) ∧ ( is_arraytype((st[r0 -- sk, val][r -- _type]) .type) → is_indexkey((sk0 ' + sks0) .first) ∧ 0 ≤ (sk0 ' + sks0) .first .index ∧ (sk0 ' + sks0) .first .index < (st[r0 -- sk, val][r -- _length]) .intval) ∧ fits((st[r0 -- sk, val][r -- (sk0 ' + sks0) .first]) .refval, (sk0 ' + sks0) .rest, st[r0 -- sk, val]) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk0]) ∧ (is_classtype(st[r -- _type] .type) → sk0 ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sk0) ∧ ¬ sk0 .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sk0 .index) ∧ fits(st[r -- sk0] .refval, sks0, st), ∃ sks, sks1. sk0 ' + sks0 = sks + sk ' + sks1 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks3. sks3 + sk ' ⊑ sks → st[r -- sks3] .refval ≠ st[r -- sks] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
∀ r, st, r0, sk, val. (fits(r, sks0, st[r0 -- sk, val]) ↔ fits(r, sks0, st)) ∨ sk = _length ∨ sk = _type ∨ (∃ sks2, sks1. sks0 = sks2 + sk ' + sks1 ∧ st[r -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + sk ' ⊑ sks2 → st[r -- sks3] .refval ≠ st[r -- sks2] .refval)), is_classtype(st[r -- _type] .type) → sk0 ∈ instfields(st[r -- _type] .type .class) ⊦ r = jvmref, sk = _length, sk = _type, is_referencevalue(st[r0 -- sk, val][r -- sk0]) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r -- _length] .intval) ∧ fits((st[r0 -- sk, val][r -- sk0]) .refval, sks0, st[r0 -- sk, val]) ↔ is_referencevalue(st[r -- sk0]) ∧ (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sk0) ∧ ¬ sk0 .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sk0 .index) ∧ fits(st[r -- sk0] .refval, sks0, st), ∃ sks, sks1. sk0 ' + sks0 = sks + sk ' + sks1 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks3. sks3 + sk ' ⊑ sks → st[r -- sks3] .refval ≠ st[r -- sks] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []], [CSIMPNAMEDSEQ : list, storekeys, c-07, ⊦ (sk ' + sks) .rest = sks], [CSIMPNAMEDSEQ : javastore, , at-other-16, ⊦ sk ≠ sk0 → (st[r -- sk, val] [r0 -- sk0 ] ) = st[r0 -- sk0]], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, c-08, ⊦ (sk ' + sks) .first = sk])]]