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Proof step 31 from proof validrefs-append (previous step)

acc + r ' = r1 ' + refs, st[r0 -- i '] = refval(r1), is_array(str, r0, st), validrefs(str, r ' + refs0, ty0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, acc + r ' + refs0, st[r0 -- _type] .type .type, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

User applied rule insert equation

And obtained the following new goals

Proof step 30:
acc + r ' = r1 ' + refs, st[r0 -- i '] = refval(r1), is_array(str, r0, st), validrefs(str, r ' + refs0, ty0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, validrefs(str, acc + r ', st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, acc + r ' + refs0, st[r0 -- _type] .type .type, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[inserteqarg: pos: left 1,T,F,()]

Additional information

[[CONCRETESIMPRULES : ()]]