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Proof step 81 from proof validrefs-subset-equiv (previous step)

st[r -- i '] = refval(r0), r ∈ st, 0 ≤ i, 0 < st0[r -- _length] .intval, is_array(str, r, st), st[r -- _type] .type ≤ ty, st ⊆ st0, st0[r -- _type] .type ≤ ty, i < st0[r -- _length] .intval, validrefs(str, r0 ' + refs1, st0[r -- _type] .type .type, st0), r -- i ' ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), ¬ st[r -- _length] .intval ≤ i ∧ validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 80:
r -- _length ∈ st ∧ st ⊆ st0, st[r -- i '] = refval(r0), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), st[r -- _type] .type ≤ ty, st ⊆ st0, st0[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st0[r -- _type] .type .type, st0), r -- i ' ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), ¬ st[r -- _length] .intval ≤ i ∧ validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)

Rule argument

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

Additional information

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