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Proof step 43 from proof fits-subset (previous step)

st[r -- i '] = refval(r0), r -- _type ∈ st0, is_array(str, r, st0), st0 ⊆ st, fits(r0, sks0, st), is_arraytype(st0[r -- _type] .type), i < st[r -- _length] .intval, r ∈ st0, 0 < st[r -- _length] .intval, 0 ≤ i, ∀ st0, st, r, str. st0 ⊆ st ∧ fits(r, sks0, st) → junkref(str, r, st0) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st0), is_referencevalue(st0[r -- i ']) ∧ ¬ st0[r -- _length] .intval ≤ i ∧ fits(st0[r -- i '] .refval, sks0, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 42:
r -- _length ∈ st0 ∧ st0 ⊆ st, st[r -- i '] = refval(r0), r -- _type ∈ st0, is_array(str, r, st0), st0 ⊆ st, fits(r0, sks0, st), is_arraytype(st0[r -- _type] .type), i < st0[r -- _length] .intval, r ∈ st0, 0 < st0[r -- _length] .intval, 0 ≤ i, ∀ st0, st, r, str. st0 ⊆ st ∧ fits(r, sks0, st) → junkref(str, r, st0) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st0), is_referencevalue(st0[r -- i ']) ∧ ¬ st0[r -- _length] .intval ≤ i ∧ fits(st0[r -- i '] .refval, sks0, st0)

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [r -- _length, st0, st] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r -- _length ∈ st → ¬ is_array(str, r, st)])], [EXTRATERMS : (r -- _length, st0, st)]]