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Proof step 25 from proof validref-refs-last-valid-subset (previous step)

st0[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), r0 -- _type ∈ st, ty ≤ ty0, i < i0, 0 ≤ i, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, 0 ≤ i0, r0 ∈ st, type∃(str, ty), okreftype(refval(r0), mkarraytype(ty), st), 0 ≤ st[r0 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → r0 -- j ' ∈ st ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r0 = jvmref, r0 -- i ' ∈ st, noval .refval ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ rk ∈ st ∧ st[rk] ≠ st1[rk] → ¬ st ⊆ st1
Proof step 24:
¬ (r0 -- _length ∈ st ∧ st[r0 -- _length] ≠ st0[r0 -- _length]), st0[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), r0 -- _type ∈ st, ty ≤ ty0, i < i0, 0 ≤ i, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, 0 ≤ i0, r0 ∈ st, type∃(str, ty), okreftype(refval(r0), mkarraytype(ty), st), 0 ≤ st[r0 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → r0 -- j ' ∈ st ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r0 = jvmref, r0 -- i ' ∈ st, noval .refval ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st[rk] ≠ st1[rk] → ¬ st ⊆ st1 ,[rk, st, st1] → [r0 -- _length, st, st0] ,F ,store ,javastore-ostorea ,subset-elem-eq-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0 -- _length, st, st0)]]