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Proof step 15 from proof validrefs-subset (previous step)

st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st[r0 -- _type] = st0[r0 -- _type], st[r -- _type] .type ≤ ty1, r0 -- mkfs(class, ty1, fieldvar) ' ∈ st0, validrefs(str, r ' + refs, ty1, st0), mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), st0[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st0), is_obj(str, r0, st), r0 -- _type ∈ st, r0 -- _type ∈ st0, r0 ∈ st, r0 ∈ st0, r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, rk ∈ st, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, r0 = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty1, st), rk ∈ st0 ∧ st[rk] = st0[rk]

User applied rule all left

And closed the goal!

Rule argument

[EXRARG : pos: left 17, [extquanttermlist: (rk)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (rk)]]