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

st0[r -- _type] .type = mkclasstype(class0), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r -- _type] = st0[r -- _type], is_obj(str, r, st0), is_obj(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), validrefs(str, r1 ' + refs, ty0, st), is_classtype(st0[r -- _type] .type), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r1 ' + refs, ty0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
st[r -- _type] = st0[r -- _type], st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), st0[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), is_obj(str, r, st0), validrefs(str, r1 ' + refs, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), unchangedNorec(r, st, st0), is_classtype(ty), class0 ≤ ty .class, ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2) ⊦ r = jvmref, validrefs(str, r1 ' + refs, ty0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]