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Proof step 35 from proof validrefs-addobj-junkref (previous step)

validrefs(str, r1 ' + r2 ' + refs, ty0, addobj(r, class, fis, st)), newref(r, st), is_obj(str, r1, st) ∨ is_array(str, r1, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty, r0, class0, fis0, st0. validrefs(str0, r2 ' + refs, ty, addobj(r0, class0, fis0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs

User applied rule case distinction

And obtained the following new goals

Proof step 20:
is_obj(str, r1, st), validrefs(str, r1 ' + r2 ' + refs, ty0, addobj(r, class, fis, st)), newref(r, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty, r0, class0, fis0, st0. validrefs(str0, r2 ' + refs, ty, addobj(r0, class0, fis0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs
Proof step 34:
is_array(str, r1, st), validrefs(str, r1 ' + r2 ' + refs, ty0, addobj(r, class, fis, st)), newref(r, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty, r0, class0, fis0, st0. validrefs(str0, r2 ' + refs, ty, addobj(r0, class0, fis0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]