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Proof step 8 from proof validref-put-samefield (previous step)

r ∈ st, oktype(val, ty, st), oktype(st[r -- mkfs(class, ty, fieldvar) '], ty, st), r -- mkfs(class, ty, fieldvar) ' ∈ st, is_obj(r, st[r -- mkfs(class, ty, fieldvar) ', val]) ∨ is_array(r, st[r -- mkfs(class, ty, fieldvar) ', val]) ⊦ mkfs(class, ty, fieldvar) ' = _length, mkfs(class, ty, fieldvar) ' = _type, is_array(r, st), is_obj(r, st)

User applied rule case distinction

And obtained the following new goals

Proof step 5:
is_obj(r, st[r -- mkfs(class, ty, fieldvar) ', val]), r ∈ st, oktype(val, ty, st), oktype(st[r -- mkfs(class, ty, fieldvar) '], ty, st), r -- mkfs(class, ty, fieldvar) ' ∈ st ⊦ mkfs(class, ty, fieldvar) ' = _length, mkfs(class, ty, fieldvar) ' = _type, is_array(r, st), is_obj(r, st)
Proof step 7:
is_array(r, st[r -- mkfs(class, ty, fieldvar) ', val]), r ∈ st, oktype(val, ty, st), oktype(st[r -- mkfs(class, ty, fieldvar) '], ty, st), r -- mkfs(class, ty, fieldvar) ' ∈ st ⊦ mkfs(class, ty, fieldvar) ' = _length, mkfs(class, ty, fieldvar) ' = _type, is_array(r, st), is_obj(r, st)

Rule argument

[CASEDARG : pos: left 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]