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Proof step 42 from proof max-rem-notsame (previous step)

m0 < m, bag.max < m, m0 < bag.max, m0 + 1 < m, ∀ m1. bag.max < m1 → count(m1, bag) = 0 ⊦ bag = ∅, count(m, bag ++ m0) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0)
Proof step 44:
m0 + 1 < m, m0 < bag.max, bag.max < m, m0 < m, ∀ m1. bag.max < m1 → count(m1, bag) = 0 ⊦ (m = m0 ⊃ 1;0) + count(m, bag) = 0, bag = ∅

Rule argument

spec: bag-basic, inst: nat-bag name: count-insert seq: ⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0) subst: [n0, bag0, n] → [m0, bag, m] flags: <all paths>

Additional information

Used terms: m0, bag, m