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Proof step 19 from proof validref-subspec-samesubclasses-01 (previous step)

same-subclasses-contains(ty .jtelemtype .class, str, str0), tdname+∃(str0, ty .jtelemtype .class), st[r -- _type] .type ≤ ty, junkref(str, r, st), has_classtype(st[r -- _type] .type) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), st[r -- _type] .type .jtelemtype .class ≤ ty .jtelemtype .class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ has_classtype(ty) → ( ty ≤ ty0 ↔ ty .jtdims = ty0 .jtdims ∧ has_classtype(ty0) ∧ ty .jtclass ≤ ty0 .jtclass ∨ ty .jtdims > ty0 .jtdims ∧ has_classtype(ty0) ∧ ty0 .jtclass = `java.lang.Object' .class)
Proof step 18:
has_classtype(st[r -- _type] .type), same-subclasses-contains(ty .jtelemtype .class, str, str0), tdname+∃(str0, ty .jtelemtype .class), st[r -- _type] .type .jtdims = ty .jtdims ∧ has_classtype(ty) ∧ st[r -- _type] .type .jtclass ≤ ty .jtclass ∨ st[r -- _type] .type .jtdims > ty .jtdims ∧ has_classtype(ty) ∧ ty .jtclass = `java.lang.Object' .class, junkref(str, r, st), has_classtype(st[r -- _type] .type) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), st[r -- _type] .type .jtelemtype .class ≤ ty .jtelemtype .class

Rule argument

[speclemmaarg: , has_classtype(ty) → ( ty ≤ ty0 ↔ ty .jtdims = ty0 .jtdims ∧ has_classtype(ty0) ∧ ty .jtclass ≤ ty0 .jtclass ∨ ty .jtdims > ty0 .jtdims ∧ has_classtype(ty0) ∧ ty0 .jtclass = `java.lang.Object' .class) ,[ty0, ty] → [ty, st[r -- _type] .type] ,F ,typefuns , ,subtype-norec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty, st[r -- _type] .type)]]