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Proof step 8 from proof validrefs-levelsubset (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs, ty, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, is_obj(str0, r, st), ∀ str1, ty1, st0, str2. validrefs(str1, r0 ' + refs, ty1, st0) ∧ level⊆(str1, str2) → validrefs(str2, r0 ' + refs, ty1, st0) ⊦ r = jvmref, mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ r0 = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str0, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, mkfs(class, ty, fieldvar) .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(str0, r, st), st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs, ty, st), ∀ str1, ty1, st0, str2. validrefs(str1, r0 ' + refs, ty1, st0) ∧ level⊆(str1, str2) → validrefs(str2, r0 ' + refs, ty1, st0) ⊦ r = jvmref, validrefs(str0, r0 ' + refs, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty])]]