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Proof step 16 from proof update-ex-nodups (previous step)

∀ r, st. ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fis0 ⊦ ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fv + fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fv + fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ update(r, fv ' + fis, st) = (update(r, fis, st)[r -- fv .1, fv .2])
Proof step 15:
∀ r, st. ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fis0 ⊦ ∃ fis. ¬ dups(fis .keys) ∧ (update(r, fis0, st)[r -- fv .1, fv .2]) = update(r, fis, st) ∧ fis ⊆ fv ' + fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]