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Proof step 13 from proof validstatfields-subset (previous step)

sk .fs = mkfs(class0, ty, fieldvar), st ⊆ st0, init(str, st), init(str, st0), sk ∈ statfields(class), initdone(class, st0), tdname∃(str, class), initdone(class, st) → validstatfield(str, sk, st) ⊦ validstatfield(str, sk, st0), validstatfield(str, sk, st) ∧ initdone(class0, st0) ∧ initdone(class0, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
sk = fs ' ∧ is_fskey(sk), fs = mkfs(class0, ty, fieldvar), st ⊆ st0, init(str, st), init(str, st0), sk ∈ statfields(class), initdone(class, st0), tdname∃(str, class), initdone(class, st) → validstatfield(str, sk, st) ⊦ validstatfield(str, sk, st0), validstatfield(str, sk, st) ∧ initdone(class0, st0) ∧ initdone(class0, st)

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: elim-03 antecedent: succedent: is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') substlist: [sk, fs] → [sk, fs] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : storekey, , test-01, ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPNAMEDSEQ : addfuns, , statfields-index-01, ⊦ is_indexkey(sk) → ¬ sk ∈ statfields(class)], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]