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Proof step 164 from proof validrefs-all-same (conclusion)

⊦ 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. 0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st0[r -- i ']))) → validrefs(str, refs, ty, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 163:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]