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Proof step 19 from proof arrayMaxWhile (previous step)

st[a -- i1 '] .intval = max(getintarray(a, st)), st[_mode] = noval, st[a -- i0 '] .intval ≤ st[a -- i2 '] .intval, 0 < st[a -- _length] .intval, 1 < st[a -- _length] .intval, i1 < st[a -- _length] .intval, is_integervalue(st[a -- i0 ']), is_integervalue(st[a -- 0 ']), is_integervalue(st[a -- i2 ']), is_integervalue(st[a -- i1 ']), 0 ≤ i2, init(st), okarray(a, int_type, st), i0 ≤ i1, i1 ≤ i2, 0 ≤ i0, 0 ≤ i1, i0 < i2, 0 < i2, is_integervalue(st[a -- 1 ']), i0 < st[a -- _length] .intval, i2 < st[a -- _length] .intval, max(getintarray(a, st)) ∈ getintarray(a, st), ∀ i. i ∈ getintarray(a, st) → i ≤ max(getintarray(a, st)) ⊦ i0 = i2, getintarray(a, st) = [], a = jvmref, ∃ i3. ¬ i3 ≤ i0 ∧ i3 ≤ i2 ∧ st[a -- i3 '] .intval = max(getintarray(a, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i ∈ getintarray(r, st) ↔ (∃ j. i = st[r -- j '] .intval ∧ 0 ≤ j ∧ j < st[r -- _length] .intval)
Proof step 18:
st[a -- i1 '] .intval = max(getintarray(a, st)), st[_mode] = noval, st[a -- i0 '] .intval ≤ st[a -- i2 '] .intval, 0 < st[a -- _length] .intval, 1 < st[a -- _length] .intval, i1 < st[a -- _length] .intval, is_integervalue(st[a -- i0 ']), is_integervalue(st[a -- 0 ']), is_integervalue(st[a -- i2 ']), is_integervalue(st[a -- i1 ']), 0 ≤ i2, init(st), okarray(a, int_type, st), i0 ≤ i1, i1 ≤ i2, 0 ≤ i0, 0 ≤ i1, i0 < i2, 0 < i2, is_integervalue(st[a -- 1 ']), i0 < st[a -- _length] .intval, i2 < st[a -- _length] .intval, ∃ j. max(getintarray(a, st)) = st[a -- j '] .intval ∧ 0 ≤ j ∧ j < st[a -- _length] .intval, ∀ i. i ∈ getintarray(a, st) → i ≤ max(getintarray(a, st)) ⊦ i0 = i2, getintarray(a, st) = [], a = jvmref, ∃ i3. ¬ i3 ≤ i0 ∧ i3 ≤ i2 ∧ st[a -- i3 '] .intval = max(getintarray(a, st))

Rule argument

[x0lemmaarg: spec-name: storearrays instance-name: lemma-name: getintarray-in antecedent: succedent: i ∈ getintarray(r, st) ↔ (∃ j. i = st[r -- j '] .intval ∧ 0 ≤ j ∧ j < st[r -- _length] .intval) substlist: [st, r, i] → [st, a, max(getintarray(a, st))] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 22)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, a, max(getintarray(a, st)))]]