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Proof step 35 from proof validrefnotnull-union-at-right (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
sk = fs ', fs = mkfs(class1, ty, fieldvar), st0[r -- _type] .type = mkclasstype(class0), validref(str, r, mkclasstype(class), st0), sk ∈ instfields(class), is_fskey(sk) ⊦ st[r -- sk] = noval, r = jvmref, r -- sk ∈ st0, mkfs(class1, ty, fieldvar) ' ∈ instfields(class0) ∧ (is_reftype(ty) ∨ ty = abstract_type) ∧ st0[r -- mkfs(class1, ty, fieldvar) '] .refval ≠ jvmref ∧ ( ¬ is_referencevalue(st0[r -- mkfs(class1, ty, fieldvar) ']) ∨ ¬ st0[r -- (mkfs(class1, ty, fieldvar) ' ' + _type ')] .type ≤ ty ∨ ¬ validref(str, st0[r -- mkfs(class1, ty, fieldvar) '] .refval, ty, st0))

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]