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Proof step 7 from proof validFields-empty-01 (previous step)

hasKeys(r, fis .keys, ∅), unique_al(fis) ⊦ fis = [], _type ∈ fis, _length ∈ fis

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ (fis + fis0) .keys = fis .keys + fis0 .keys
Proof step 4:
⊦ fv ' .keys = fv .1 '
Proof step 5:
⊦ hasKeys(r, sks + sks0, st) ↔ hasKeys(r, sks, st) ∧ hasKeys(r, sks0, st)
Proof step 6:
⊦ hasKeys(r, sk ', st) ↔ r -- sk ∈ st

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis], [CSIMPSEQ : ⊦ fv ' + fis ≠ []], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ ¬ rk ∈ ∅], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]