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Proof step 54 from proof validfieldinits-def-01 (previous step)

∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey((sk0 × val) .1) ∧ validval(str, (sk0 × val) .2, (sk0 × val) .1 .fs .type, st) ∧ type∃(str, (sk0 × val) .1 .fs .type) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey(sk0) ∧ validval(str, val, sk0 .fs .type, st) ∧ type∃(str, sk0 .fs .type) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]