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Proof step 49 from proof ex-fits-validrefs-stronger (previous step)

# refs = # sks0, st[r -- sk] = refval(r0), st[r -- _type] .type = mkclasstype(class), sk ∈ 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, r ' + r0 ' + refs, mkclasstype(class), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 48:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(class), # refs = # sks0, st[r -- sk] = refval(r0), st[r -- _type] .type = mkclasstype(class), sk ∈ 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), r0 ' + refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs) .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs, fs .type, st))

Rule argument

[speclemmaarg: , is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st))) ,[st, ty, refs, r, str] → [st, mkclasstype(class), r0 ' + refs, r, str] ,F ,cyclic , ,validrefs-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2], [CSIMPSEQ : ⊦ class ≤ class])], [EXTRATERMS : (st, mkclasstype(class), r0 ' + refs, r, str)]]