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Proof step 163 from proof validrefs-all-same (previous step)

validrefs(str, refs, ty, st), ∀ r. r ∈ refs ∧ r ≠ jvmref → st[r -- _type] = st0[r -- _type] ∧ (is_classtype(st[r -- _type] .type) → (∀ sk. sk ∈ instfields(st[r -- _type] .type .class) → st[r -- sk] = st0[r -- sk])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '])) ⊦ validrefs(str, refs, ty, st0)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ validrefs(str, [], ty, st)
Proof step 162:
∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 ∧ r ≠ jvmref → st[r -- _type] = st0[r -- _type] ∧ (is_classtype(st[r -- _type] .type) → (∀ sk. sk ∈ instfields(st[r -- _type] .type .class) → st[r -- sk] = st0[r -- sk])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i ']))) → validrefs(str, refs0, ty, st0), validrefs(str, r + refs0, ty, st), ∀ r0. r0 ∈ r + refs0 ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])) ⊦ validrefs(str, r + refs0, ty, st0)

Rule argument

[VARWITHVARSEQSARG : refs, ()]

Additional information

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