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Proof step 2 from proof in-put-keys-02 (previous step)

⊦ str = str0, r0 -- mkfs(class, ty, str .field) ' ∈ st[r -- (sks + mkfs(class0, ty0, str0 .field) ' '), val] ↔ r0 -- mkfs(class, ty, str .field) ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sk ≠ sk0 → (r0 -- sk0 ∈ st[r -- (sks + sk '), val] ↔ r0 -- sk0 ∈ st)

Rule argument

[crewrite-arg: in-put-keys , F , [val, sk, sks, r, st, sk0, r0] → [val, mkfs(class0, ty0, str0 .field) ', sks, r, st, mkfs(class, ty, str .field) ', r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0])], [EXTRATERMS : (val, mkfs(class0, ty0, str0 .field) ', sks, r, st, mkfs(class, ty, str .field) ', r0)]]