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Proof step 11 from proof validrefs-maxlen (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_obj(str, r, st), validrefs(str, r0 ' + refs, ty1, 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 7:
validrefs(str, r0 ' + refs, ty1, st -- r), st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_obj(str, r, st), validrefs(str, r0 ' + refs, ty1, st -- r) → # refs ≤ # (st .refs -- r) ⊦ r = r0, r = jvmref, r ∈ refs, r0 ∈ refs, dups(refs)
Proof step 10:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_obj(str, r, st), validrefs(str, r0 ' + refs, ty1, st -- r) → # refs ≤ # (st .refs -- r) ⊦ validrefs(str, r0 ' + refs, ty1, st -- r), r = r0, r = jvmref, r ∈ refs, r0 ∈ refs, dups(refs)

Rule argument

[fma-arg: validrefs(str, r0 ' + refs, ty1, st -- r)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (validrefs(str, r0 ' + refs, ty1, st -- r))]]