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Proof step 29 from proof validrefs-maxlen (previous step)

st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st -- r) → # refs ≤ # (st .refs -- r) ⊦ r = r0, r = jvmref, r ∈ refs, r0 ∈ refs, dups(refs)

User applied rule cut formula

And obtained the following new goals

Proof step 25:
validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st -- r), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st -- r) → # refs ≤ # (st .refs -- r) ⊦ r = r0, r = jvmref, r ∈ refs, r0 ∈ refs, dups(refs)
Proof step 28:
st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st -- r) → # refs ≤ # (st .refs -- r) ⊦ validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st -- r), r = r0, r = jvmref, r ∈ refs, r0 ∈ refs, dups(refs)

Rule argument

[fma-arg: validrefs (str, r0 ' + refs, st[r -- _type] .type .type, st -- r) ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (validrefs (str, r0 ' + refs, st[r -- _type] .type .type, st -- r))]]