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Proof step 35 from proof validrefs-addarray (previous step)

¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, addarray(r, ty0, vals, st)) ∨ ¬ (addarray(r, ty0, vals, st)[r0 -- _type]) .type ≤ ty)), newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 34:
newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), is_valid_ref(str, r0, addarray(r, ty0, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (addarray(r, ty, vals, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]