Nuprl Lemma : int_hgrp_to_nat_wf
∀[n:|(<ℤ+>↓hgrp)|]. (nat(n) ∈ ℕ)
Proof
Definitions occuring in Statement :
int_hgrp_to_nat: nat(n),
int_add_grp: <ℤ+>,
hgrp_of_ocgrp: g↓hgrp,
grp_car: |g|,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
int_hgrp_to_nat: nat(n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
grp_car_subtype,
grp_car_wf,
hgrp_of_ocgrp_wf,
int_add_grp_wf2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
thin,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination
Latex:
\mforall{}[n:|(<\mBbbZ{}+>\mdownarrow{}hgrp)|]. (nat(n) \mmember{} \mBbbN{})
Date html generated:
2016_05_15-PM-00_19_35
Last ObjectModification:
2015_12_26-PM-11_37_27
Theory : groups_1
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