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Proof step 111 from proof validrefs-not-contains (previous step)

¬ (r1 ≠ jvmref ∧ (¬ is_valid_ref(str, r1, st) ∨ ¬ st[r1 -- _type] .type ≤ st[r -- _type] .type .type)), st[r -- i '] = refval(r1), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0 + r1 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type) ⊦ r1 = jvmref, r = r1, r = jvmref, ∃ ty1. ty1 ≤ st[r -- _type] .type ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r1 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r1 -- _type] .type ≤ ty1 .type) ∧ type∃(str, st[r1 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 110:
st[r -- i '] = refval(r1), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0 + r1 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ st[r -- _type] .type .type ⊦ r1 = jvmref, r = r1, r = jvmref, ∃ ty1. ty1 ≤ st[r -- _type] .type ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r1 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r1 -- _type] .type ≤ ty1 .type) ∧ type∃(str, st[r1 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]