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Proof step 26 from proof isarray-addarray-01 (previous step)

r1 ≠ jvmref ∧ r1 -- _type ∈ addarray(r0, ty, vals, st) ∧ is_typevalue(addarray(r0, ty, vals, st)[r1 -- _type]) ∧ is_arraytype((addarray(r0, ty, vals, st)[r1 -- _type]) .type) ∧ okarray(r1, (addarray(r0, ty, vals, st)[r1 -- _type]) .type .type, addarray(r0, ty, vals, st)) ⊦ r1 = r0, is_array(r1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 4:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 5:
⊦ r ≠ r0 → (r ∈ addarray(r0, ty0, vals, st) ↔ r ∈ st)
Proof step 25:
okarray(r1, st[r1 -- _type] .type .type, addarray(r0, ty, vals, st)), is_arraytype(st[r1 -- _type] .type), is_typevalue(st[r1 -- _type]), r1 -- _type ∈ st, r1 ∈ st ⊦ r1 = jvmref, r1 = r0, is_array(r1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ okarray(r, ty, st) → r ≠ jvmref ∧ r ∈ st])]]