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Proof step 6 from proof validrefnotnull-array-len-subset (previous step)

st ⊆ st0, validrefnotnull(`docs2store', r, mkarraytype(byte_type), st) ⊦ r = jvmref, st[r -- _length] .intval = st0[r -- _length] .intval, r -- _length ∈ st ∧ st[r -- _length] ≠ st0[r -- _length]

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
⊦ validrefnotnull(str, r, mkarraytype(ty), st) → is_integervalue(st[r -- _length])
Proof step 5:
⊦ validrefnotnull(str, r, mkarraytype(ty), st) → is_integervalue(st[r -- _length])

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [st[r -- _length], i] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ intval(i) ≠ noval], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r -- _length], i)]]