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Proof step 11 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), is_array(str, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, mkarraytype(ty), st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ r0 = (r0 ' + refs0) .last, r0 = jvmref, r0 ∈ refs0, dups(refs0), path∃(str, r0, (r0 ' + refs0) .last, st), path∃(str, r2, (r0 ' + refs0) .last, st), is_array(str, r0, st[r0 -- i ', refval(r2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_array(str, r, st) ∧ okval(val, st[r -- _type] .type .type) → is_array(str, r, st[r -- i ', val])
Proof step 10:
¬ (is_array(str, r0, st) ∧ okval(refval(r2), st[r0 -- _type] .type .type)), st[r0 -- _type] .type = mkarraytype(ty), is_array(str, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, mkarraytype(ty), st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ r0 = (r0 ' + refs0) .last, r0 = jvmref, r0 ∈ refs0, dups(refs0), path∃(str, r0, (r0 ' + refs0) .last, st), path∃(str, r2, (r0 ' + refs0) .last, st), is_array(str, r0, st[r0 -- i ', refval(r2)])

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: is_array-put-okval antecedent: succedent: is_array(str, r, st) ∧ okval(val, st[r -- _type] .type .type) → is_array(str, r, st[r -- i ', val]) substlist: [val, i, st, r, str] → [refval(r2), i, st, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 6)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r2), i, st, r0, str)]]