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Proof step 42 from proof validrefs-addobj-01 (previous step)

fis .keys = instfields(class), unique_al(fis), is_obj(str, r, addobj(r, class, fis, st)), validFields(r, fis, addobj(r, class, fis, st)), newref(r, st), class+∃(str, class), validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), validrefs(str, r0 ' + refs0, ty, st), validref(str, r0, ty0, addobj(r, class, fis, st)), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty ⊦ is_reftype(ty0), r0 = r, r = jvmref, r0 = jvmref, validrefs(str, r0 ' + refs0, ty0, st), is_abstract(class), validrefs(str, r0 ' + refs0, ty0, addobj(r, class, fis, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
⊦ ¬ is_reftype(ty) → (validrefs(str, refs, ty, st) ↔ refs = [] ∨ refs = jvmref ')
Proof step 41:
fis .keys = instfields(class), unique_al(fis), is_obj(str, r, addobj(r, class, fis, st)), validFields(r, fis, addobj(r, class, fis, st)), newref(r, st), class+∃(str, class), validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), validrefs(str, r0 ' + refs0, ty, st), validref(str, r0, ty0, addobj(r, class, fis, st)), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty ⊦ r0 = r, r = jvmref, r0 = jvmref, r0 ' + refs0 = jvmref ', is_abstract(class), is_reftype(ty0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]