Nuprl Lemma : mon_nat_op_add
∀[g:IMonoid]. ∀[e:|g|]. ∀[a,b:ℕ]. (((a + b) ⋅ e) = ((a ⋅ e) * (b ⋅ e)) ∈ |g|)
Proof
Definitions occuring in Statement :
mon_nat_op: n ⋅ e,
imon: IMonoid,
grp_op: *,
grp_car: |g|,
nat: ℕ,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
add: n + m,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_nat_op: n ⋅ e
Lemmas referenced :
nat_op_add
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[g:IMonoid]. \mforall{}[e:|g|]. \mforall{}[a,b:\mBbbN{}]. (((a + b) \mcdot{} e) = ((a \mcdot{} e) * (b \mcdot{} e)))
Date html generated:
2016_05_15-PM-00_16_58
Last ObjectModification:
2015_12_26-PM-11_39_05
Theory : groups_1
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