Nuprl Lemma : grp_id_wf2
∀[g:OGrp]. (e ∈ |g|+)
Proof
Definitions occuring in Statement :
hgrp_car: |g|+,
ocgrp: OGrp,
grp_id: e,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hgrp_car: |g|+,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
prop: ℙ,
subtype_rel: A ⊆r B,
omon: OMon,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Lemmas referenced :
grp_id_wf,
grp_leq_wf,
ocgrp_wf,
grp_leq_weakening_eq,
subtype_rel_sets,
abmonoid_wf,
ulinorder_wf,
grp_car_wf,
assert_wf,
infix_ap_wf,
bool_wf,
grp_le_wf,
equal_wf,
grp_eq_wf,
eqtt_to_assert,
cancel_wf,
grp_op_wf,
uall_wf,
monot_wf,
inverse_wf,
grp_inv_wf,
omon_properties,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
instantiate,
setEquality,
productEquality,
lambdaEquality,
functionEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
cumulativity,
universeEquality,
independent_pairFormation,
addLevel,
levelHypothesis
Latex:
\mforall{}[g:OGrp]. (e \mmember{} |g|\msupplus{})
Date html generated:
2017_10_01-AM-08_15_24
Last ObjectModification:
2017_02_28-PM-02_00_27
Theory : groups_1
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