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Proof step 6 from proof middle-coef-not-one-01 (previous step)

binom_coef(2 * i, i) < 2, binom_coef(2 * i, 1) ≤ binom_coef(2 * i, i), 1 < i, 0 < i, binom_coef(2 * i, 1) < 2 ⊦ i = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: coef-one seq: ⊦ 0 < i → binom_coef(i, 1) = i subst: [i] → [2 * i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%nummult-ls: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i); from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: 2 * i