Nuprl Lemma : omon_subtype
OMon ⊆r AbDMon
Proof
Definitions occuring in Statement :
omon: OMon,
abdmonoid: AbDMon,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
mon: Mon,
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
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,
cand: A c∧ B,
omon: OMon,
abmonoid: AbMon,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
abdmonoid: AbDMon,
dmon: DMon
Lemmas referenced :
mon_wf,
comm_wf,
grp_car_wf,
grp_op_wf,
eqfun_p_wf,
grp_eq_wf,
ulinorder_wf,
assert_wf,
infix_ap_wf,
bool_wf,
grp_le_wf,
equal_wf,
eqtt_to_assert,
omon_properties,
set_wf,
sq_stable__comm,
subtype_rel_sets
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
setEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
cumulativity,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
because_Cache,
lambdaEquality,
lambdaFormation,
productEquality,
sqequalRule,
applyEquality,
universeEquality,
instantiate,
functionEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
OMon \msubseteq{}r AbDMon
Date html generated:
2017_10_01-AM-08_14_22
Last ObjectModification:
2017_02_28-PM-01_58_56
Theory : groups_1
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