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Proof step 9 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), st[r0 -- _type] .type ≤ ty0, is_valid_ref(str, r0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, type∃(str, st[r0 -- _type] .type) ⊦ r = jvmref, r = r0, r0 = jvmref, (∃ fs. fs ' ∈ instfields(class0) ∧ st[r0 -- _type] .type ≤ fs .type) ∧ ¬ interface∃(str, class0)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), st[r0 -- _type] .type ≤ ty0, is_valid_ref(str, r0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, type∃(str, st[r0 -- _type] .type) ⊦ ∃ fs. fs ' ∈ instfields(class0) ∧ st[r0 -- _type] .type ≤ fs .type, r = jvmref, r = r0, r0 = jvmref
Proof step 8:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), st[r0 -- _type] .type ≤ ty0, is_valid_ref(str, r0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, type∃(str, st[r0 -- _type] .type) ⊦ ¬ interface∃(str, class0), r = jvmref, r = r0, r0 = jvmref

Rule argument

[CASEDARG : pos: right 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]