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Proof step 44 from proof isarray-put-array-badindex (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty)), i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ r0 = jvmref, is_typevalue(typeval(mkarraytype(ty))) ∧ is_arraytype(typeval(mkarraytype(ty)) .type) ∧ typeval(mkarraytype(ty)) .type .type ≤ ty ∧ r0 -- _length ∈ st[r -- i ', val] ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)) ↔ okarray(r0, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 43:
st[r0 -- _type] = typeval(mkarraytype(ty)), i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ r0 = jvmref, is_typevalue(typeval(mkarraytype(ty))) ∧ is_arraytype(typeval(mkarraytype(ty)) .type) ∧ typeval(mkarraytype(ty)) .type .type ≤ ty ∧ r0 -- _length ∈ st[r -- i ', val] ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)) ↔ okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], ty, st))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: okarrayNotNull antecedent: succedent: okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st)) substlist: [st, ty, r] → [st, ty, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r0)]]