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Proof step 82 from proof validrefs-put-notin-01 (conclusion)

⊦ ¬ r ∈ refs ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, refs + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, refs + r0 ', ty, st))

User applied rule structural induction

And obtained the following new goals

Proof step 14:
⊦ ¬ r ∈ [] ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, [] + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, [] + r0 ', ty, st))
Proof step 81:
∀ r, fs, val, st, str, r0, ty. ¬ r ∈ acc ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, acc + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, acc + r0 ', ty, st)) ⊦ ¬ r ∈ r1 + acc ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, (r1 + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 + acc) + r0 ', ty, st))

Rule argument

[VARWITHVARSEQSARG : refs, ()]

Additional information

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