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Proof step 73 from proof validrefs-put-array-badindex (previous step)

i < 0 ⊦ validrefs(str, refs, ty, st[r -- i ', val]) ↔ validrefs(str, refs, ty, st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ validrefs(str, [], ty, st)
Proof step 72:
∀ i, str, ty, st, r, val. i < 0 → (validrefs(str, refs0, ty, st[r -- i ', val]) ↔ validrefs(str, refs0, ty, st)), i < 0 ⊦ validrefs(str, r0 + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 + refs0, ty, st)

Rule argument

[VARWITHVARSEQSARG : refs, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : references generated by [], +;])]]