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Proof step 64 from proof validrefs-subset-equiv (previous step)

st0[r -- i '] = refval(r0), validrefs(str, r0 ' + refs1, st0[r -- _type] .type .type, st0), i < st0[r -- _length] .intval, st0[r -- _type] .type ≤ ty, st ⊆ st0, st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 < st0[r -- _length] .intval, 0 ≤ i, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), r -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ ¬ r -- i ' ∈ st ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r ≠ jvmref → ¬ is_array(str, r, st)
Proof step 63:
¬ (¬ r -- i ' ∈ st ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r ≠ jvmref), st0[r -- i '] = refval(r0), validrefs(str, r0 ' + refs1, st0[r -- _type] .type .type, st0), i < st0[r -- _length] .intval, st0[r -- _type] .type ≤ ty, st ⊆ st0, st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 < st0[r -- _length] .intval, 0 ≤ i, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), r -- i ' ∈ st

Rule argument

[speclemmaarg: , ¬ r -- i ' ∈ st ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r ≠ jvmref → ¬ is_array(str, r, st) ,[r, i, st, str] → [r, i, st, str] ,F ,okfuns , ,is_array-notin-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, i, st, str)]]