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Proof step 57 from proof validrefs-subset (previous step)

st[r0 -- i '] = refval(r), st0[r0 -- i '] = refval(r), st[r0 -- _type] = st0[r0 -- _type], st[r0 -- _length] = st0[r0 -- _length], r0 -- i ' ∈ st0, r0 -- _length ∈ st, r0 -- _type ∈ st, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st0), i < st0[r0 -- _length] .intval, is_valid_ref(str, r0, st0), is_array(str, r0, st), st0[r0 -- _type] .type ≤ ty, 0 < st0[r0 -- _length] .intval, 0 ≤ i, r0 -- _type ∈ st0, r0 ∈ st, r0 ∈ st0, r0 -- _length ∈ st0, r0 -- i ' ∈ st, st[r -- _type] .type ≤ st0[r0 -- _type] .type .type, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st), junkref(str, r, st), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
st[r0 -- _length] = st0[r0 -- _length], st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- i '] = refval(r), st[r0 -- i '] = refval(r), st[r -- _type] .type ≤ st0[r0 -- _type] .type .type, r0 -- i ' ∈ st, r0 -- _length ∈ st0, r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, 0 ≤ i, 0 < st0[r0 -- _length] .intval, st0[r0 -- _type] .type ≤ ty, is_array(str, r0, st), is_valid_ref(str, r0, st0), i < st0[r0 -- _length] .intval, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st0), r0 -- _type ∈ st, r0 -- _length ∈ st, r0 -- i ' ∈ st0, rk ∈ st, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, r0 = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st), rk ∈ st0 ∧ st[rk] = st0[rk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]