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Proof step 40 from proof bitsand-cast-05 (previous step)

# bits = # bits1 ⊦ sgn(bitsand(bits, false ' + bits1)) = sgn(bitsand(boolvar ' + bits, false ' + bits1)), bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ # bits = # bits0 ∧ 1 < # bits → bitsand(bits, bits0) = (bits.first ∧ bits0.first)' + bitsand(bits.rest, bits0.rest)
Proof step 42:
#(boolvar ' + bits) = #(false ' + bits1) ∧ 1 < #(boolvar ' + bits), # bits = # bits1 ⊦ sgn(bitsand(bits, false ' + bits1)) = sgn(((boolvar ' + bits).first ∧ (false ' + bits1).first)' + bitsand((boolvar ' + bits).rest, (false ' + bits1).rest)), bits1 = []

Rule argument

name: bitsand-first-samesize rotate: F subst: [bits0, bits] → [false ' + bits1, boolvar ' + bits]

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ # [] = 0; Used terms: false ' + bits1, boolvar ' + bits