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Proof step 32 from proof coprimes-min (previous step)

min(count-i2j(1, i)) ≤ min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), 0 < i, min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ 0, min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) < i, min(count-i2j(1, i)) ≤ 0, min(count-i2j(1, i)) < i, ∀ i0. i0 ∈ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) → min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ i0 ⊦ min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i ≤ j → min(count-i2j(i, j)) = i

Rule argument

spec: inst: name: count-i2j-min seq: ⊦ i ≤ j → min(count-i2j(i, j)) = i subst: [j, i] → [i, 1] flags: rewrite, current

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i, 1