Nuprl Lemma : ocmon_wf
OCMon ∈ 𝕌'
Proof
Definitions occuring in Statement :
ocmon: OCMon,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ocmon: OCMon,
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
prop: ℙ,
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]
Lemmas referenced :
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
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
setEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
cumulativity,
universeEquality,
instantiate,
functionEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
OCMon \mmember{} \mBbbU{}'
Date html generated:
2017_10_01-AM-08_14_26
Last ObjectModification:
2017_02_28-PM-01_58_54
Theory : groups_1
Home
Index