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Proof step 35 from proof fits-put-other (previous step)

∀ 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, fits(r, sk0 ' + sks0, st[r0 -- sk, val]) ↔ fits(r, sk0 ' + 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 34:
∀ 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, fits(r, sk0 ' + sks0, 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_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r -- _length] .intval) ∧ 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

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-storekeys-rec antecedent: succedent: fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ ( is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st) substlist: [st, sks, sk, r] → [st, sks0, sk0, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 2, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks0, sk0, r)]]