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Proof step 30 from proof validrefs-junkrefs-append (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, st[r -- _type] .type .type, st)), junkrefs(str, refs0 .last ' + refs1, st[refs0 .last -- _type] .type, st), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, refs. validrefs(str0, refs0, ty0, st0) ∧ junkrefs(str0, refs0 .last ' + refs, st0[refs0 .last -- _type] .type, st0) → junkrefs(str0, refs0 + refs, ty0, st0) ⊦ refs0 = [], r = jvmref, junkrefs(str, (r ' + refs0) + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
refs0 .first = st[r -- i '] .refval, is_array(str, r, st), junkrefs(str, refs0 .last ' + refs1, st[refs0 .last -- _type] .type, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str0, ty0, st0, refs. validrefs(str0, refs0, ty0, st0) ∧ junkrefs(str0, refs0 .last ' + refs, st0[refs0 .last -- _type] .type, st0) → junkrefs(str0, refs0 + refs, ty0, st0) ⊦ refs0 = [], r = jvmref, junkrefs(str, (r ' + refs0) + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]