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Proof step 4 from proof range-cong-dups (previous step)

0 < j, i ∈ mapFun(λ i. i |%| j, ints), j < n→i(# ints), 0 ≤ j ⊦ ints = [], # ints = 1, dups(ints), 0 ≤ i ∧ i < j, ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ∈ mapFun(intfun, ints) ↔ (∃ j. j ∈ ints ∧ intfun(j) = i)

Rule argument

spec: intlist inst: name: map-in seq: ⊦ i ∈ mapFun(intfun, ints) ↔ (∃ j. j ∈ ints ∧ intfun(j) = i) subst: [ints, intfun, i] → [ints, λ i. i |%| j, i] flags: rewrite

Additional information

Used simplifier rules: mod-pos: ⊦ 0 < j → ¬ i |%| j < 0;%mod-le-same: ⊦ 0 < j → ¬ j ≤ i |%| j;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: ints, λ i. i |%| j, i