Nuprl Lemma : int_dot_cons_lemma
∀bs,b,as,a:Top. ([a / as] ⋅ [b / bs] ~ (a * b) + as ⋅ bs)
Proof
Definitions occuring in Statement :
integer-dot-product: as ⋅ bs,
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
multiply: n * m,
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
integer-dot-product: as ⋅ bs,
cons: [a / b],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
top_wf,
spread_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}bs,b,as,a:Top. ([a / as] \mcdot{} [b / bs] \msim{} (a * b) + as \mcdot{} bs)
Date html generated:
2016_05_14-AM-06_56_09
Last ObjectModification:
2015_12_26-PM-01_14_59
Theory : omega
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