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Proof step 33 from proof validrefnotnull-union-at-right (previous step)

st0[r -- _type] .type = mkclasstype(class0), validref(str, r, mkclasstype(class), st0), mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ⊦ st[r -- mkfs(class1, ty, fieldvar) '] = noval, r = jvmref, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, mkfs(class1, ty, fieldvar) ' ∈ instfields(class0) ∧ (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ fs ' ∈ instfields(class) ∧ class0 ≤ class → fs ' ∈ instfields(class0)
Proof step 8:
¬ (mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ∧ class0 ≤ class), st0[r -- _type] .type = mkclasstype(class0), validref(str, r, mkclasstype(class), st0), mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ⊦ st[r -- mkfs(class1, ty, fieldvar) '] = noval, r = jvmref, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, mkfs(class1, ty, fieldvar) ' ∈ instfields(class0) ∧ (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref
Proof step 32:
mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ∧ class0 ≤ class, st0[r -- _type] .type = mkclasstype(class0), validref(str, r, mkclasstype(class), st0), mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ⊦ st[r -- mkfs(class1, ty, fieldvar) '] = noval, r = jvmref, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, true ∧ (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

Rule argument

[speclemmaarg: ,fs ' ∈ instfields(class) ∧ class0 ≤ class → fs ' ∈ instfields(class0) ,[fs, class, class0] → [mkfs(class1, ty, fieldvar), class, class0] ,F ,addfuns , ,instfields-subclass ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (mkfs(class1, ty, fieldvar), class, class0)]]