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Proof step 43 from proof ex-fits-validrefs-stronger (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ is_fskey(fs ')])]]