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Proof step 48 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, r ∈ refs0, dups(refs0), r0 ∈ refs0, ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ fs. fs ' ∈ instfields(class0) ∧ is_referencevalue(st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- fs ']) ∧ r = (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- fs ']) .refval ∧ validrefs(str, r ' + refs0 + r0 ', fs .type, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)])

User applied rule exists right

And obtained the following new goals

Proof step 47:
st[r0 -- _type] .type = mkclasstype(class0), is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, r ∈ refs0, dups(refs0), r0 ∈ refs0, ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)]), mkfs(class, ty, fieldvar) ' ∈ instfields(class0) ∧ is_referencevalue(st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- mkfs(class, ty, fieldvar) ']) ∧ r = (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- mkfs(class, ty, fieldvar) ']) .refval ∧ validrefs(str, r ' + refs0 + r0 ', mkfs(class, ty, fieldvar) .type, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[EXRARG : pos: right 9, [extquanttermlist: (mkfs(class, ty, fieldvar)) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (mkfs(class, ty, fieldvar))]]