[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

validrefs(str, r1 ' + r2 ' + refs, ty0, addarray(r, ty, vals, st)), newref(r, st), is_obj(str, r1, addarray(r, ty, vals, st)) ∨ is_array(str, r1, addarray(r, ty, vals, st)), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, 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, addarray(r, ty, vals, st)), validrefs(str, r1 ' + r2 ' + refs, ty0, addarray(r, ty, vals, st)), newref(r, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, 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, addarray(r, ty, vals, st)), validrefs(str, r1 ' + r2 ' + refs, ty0, addarray(r, ty, vals, st)), newref(r, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, 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 : ()]]