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Proof step 34 from proof shiftright-rec-pos (previous step)

mklist(false, i→n(i0)) + false ' + false ' + true ' = boolvar ' + bits0, mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(firstn(1, bits0)) = 0, ¬ boolvar ∧ ¬ true ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ bits ≠ [] → firstn(1, bits) = bits.first '
Proof step 36:
bits0 ≠ [], mklist(false, i→n(i0)) + false ' + false ' + true ' = boolvar ' + bits0, mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(bits0.first ') = 0, ¬ boolvar ∧ ¬ true ∈ bits0

Rule argument

seq: ⊦ bits ≠ [] → firstn(1, bits) = bits.first ' subst: [bits] → [bits0] rotate: F spec: list-del inst: bitlista name: firstN-one

Additional information

Used simplifier rules: ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' = bits + boolvar0 ' ↔ (boolvar ↔ boolvar0) ∧ bits = [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ boolvar ' ≠ []; Used terms: bits0