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Proof step 42 from proof ex-fits-validrefs-stronger (previous step)

# refs = # sks0, st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), is_obj(str, r, st), ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ r = jvmref, junkref(str, r, st), junkref(str, r0, st), validrefs(str, r0 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st)
Proof step 41:
¬ (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) ∧ st[r0 -- _type] .type ≤ ty), # refs = # sks0, st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), is_obj(str, r, st), ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ r = jvmref, junkref(str, r, st), junkref(str, r0, st), validrefs(str, r0 ' + refs, ty, st)

Rule argument

[speclemmaarg: , validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st) ,[str, refs, ty, st, ty0] → [str, r0 ' + refs, st[r0 -- _type] .type, st, ty] ,F ,cyclic , ,validrefs-superclass ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r0 ' + refs, st[r0 -- _type] .type, st, ty)]]