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Proof step 31 from proof validfieldinits-validreflist (previous step)

validfieldinits(str, (sk × val) ' + fis0, st), ∀ str, st. validfieldinits(str, fis0, st) → validreflist(str, mkjavavalues(fis0 .vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st) ⊦ validreflist(str, mkjavavalues((val ' + fis0 .vals) .nonnullrefs), mkclasstype(`java.lang.Object' .class), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ validfieldinits(str, fv ' + fis, st) ↔ is_fskey(fv .1) ∧ validval(str, fv .2, fv .1 .fs .type, st) ∧ type∃(str, fv .1 .fs .type) ∧ validfieldinits(str, fis, st)
Proof step 30:
is_fskey((sk × val) .1) ∧ validval(str, (sk × val) .2, (sk × val) .1 .fs .type, st) ∧ type∃(str, (sk × val) .1 .fs .type) ∧ validfieldinits(str, fis0, st), ∀ str, st. validfieldinits(str, fis0, st) → validreflist(str, mkjavavalues(fis0 .vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st) ⊦ validreflist(str, mkjavavalues((val ' + fis0 .vals) .nonnullrefs), mkclasstype(`java.lang.Object' .class), st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validfieldinits-rec antecedent: succedent: validfieldinits(str, fv ' + fis, st) ↔ is_fskey(fv .1) ∧ validval(str, fv .2, fv .1 .fs .type, st) ∧ type∃(str, fv .1 .fs .type) ∧ validfieldinits(str, fis, st) substlist: [st, fis, fv, str] → [st, fis0, sk × val, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk × val, str)]]